The GRIFFIN Data Acquisition System

A.B. Garnsworthya,∗, C.J. Pearsona, D. Bishopa, B. Shawa, J.K. Smitha, M. Bowrya, V. Bildsteinb,G. Hackmana, P.E. Garrettb, Y. Linna, J-P. Martinc, W.J. Millsa, C.E. Svenssonb

aPhysical Sciences Division, TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, Canada, V6T 2A3bDepartment of Physics, University of Guelph, Guelph, ON, Canada, N1G 2W1

cDepartment of Physics, Universite de Montreal, Montreal, QC, Canada

Abstract

Gamma-Ray Infrastructure For Fundamental Investigations of Nuclei, GRIFFIN, is a new experimentalfacility for radioactive decay studies at the TRIUMF-ISAC laboratory. This article describes the details ofthe custom designed GRIFFIN digital data acquisition system. The features of the system that will enablehigh-precision half-life and branching ratio measurements with levels of uncertainty better than 0.05% aredescribed. The system has demonstrated the ability to effectively collect signals from High-purity germaniumcrystals at counting rates up to 50 kHz while maintaining good energy resolution, detection efficiency andspectral quality.

Keywords: Digital electronics, digital signal processing, HPGe, TRIUMF, ISAC

1. Introduction

Large arrays of detectors for gamma-ray mea-surements coupled with auxiliary particle detectionsystems provide one of the most powerful and ver-satile tools for studying exotic nuclei through nu-clear spectroscopy at rare-isotope beam facilities.Gamma-Ray Infrastructure For Fundamental In-vestigations of Nuclei, GRIFFIN [1], is a new ex-perimental facility for radioactive decay studies atthe TRIUMF-ISAC laboratory [2] located in Van-couver, Canada.

GRIFFIN will be used for decay spectroscopy re-search with low-energy radioactive ion beams. Ahigh gamma-ray detection efficiency provided by anarray of sixteen High-Purity Germanium (HPGe)clover detectors [3], combined with the rare-isotopebeams from ISAC, will support a broad program ofresearch in the areas of nuclear structure, nuclearastrophysics, and fundamental interactions.

The data acquisition (DAQ) system for GRIFFINtakes advantage of custom-designed digital elec-tronics with many of the concepts based on theDAQ System [4] developed for the TRIUMF-ISAC

∗Corresponding author: 4004 Wesbrook Mall, Vancouver,BC, V6T 2A3, Canada

Email address: garns@triumf.ca (A.B. Garnsworthy)

Gamma-Ray Escape-Suppressed Spectrometer (TI-GRESS) array [5]. The main design goals for thesystem were to facilitate the requirements of thetwo main themes of the physics program for nuclearstructure and precision measurements relevant tothe study of Fermi superallowed beta decays. Theyare to;

• operate at high data throughput with eachHPGe crystal counting at a rate of up to 50kHz, and

• achieve a level of accountability and dead-time/event traceability consistent with half-lifeand branching ratio measurements to a preci-sion better than 0.05 %.

This article describes the hardware and firmwareaspects of the new digital data acquisition sys-tem which have been developed to meet and ex-ceed these design goals. Section 2 describes thedetector signal properties that will be processed bythe GRIFFIN DAQ system. Section 3 provides anoverview and description of the hardware compo-nents of the system. A detailed discussion of thesignal processing algorithms applied in the firmwareis provided in Section 4, followed in Section 5 by adescription of the information that these algorithmsprovide in the offline data. The user interface to the

Preprint submitted to Nuclear Instruments and Methods A November 17, 2017

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system is detailed in Section 6. The performance ofthe system for spectroscopic measurements is exam-ined in Section 7 and the features necessary for per-forming precision measurements discussed in Sec-tion 8. Finally Section 9 presents a look towardsfuture development plans and a summary is givenin Section 10.

2. Detector Properties

The signals from various radiation detector typeswill be processed by the GRIFFIN DAQ system andas such a variety of digitizer types are required. Thesignal properties of the primary detectors are shownin Table 1. Two classes of radiation detectors areconsidered; semiconductors and scintillators whichhave relatively slow and fast signals respectively.

In the initial implementation of the GRIFFINDAQ system digitizers with sampling rates of100 MHz and 1 GHz have been pursued, with 14-bit and 12-bit resolution respectively. These arecombined with other modules for data readout,clock synchronization and slow-equipment controls.These modules are described in detail in the fol-lowing section and are capable of handling the re-quirements for semiconductor and scintillator typedetectors.

3. System Overview and Hardware Descrip-tion

The MIDAS (Maximum Integrated Data Acqui-sition System) data acquisition system [6] devel-oped at PSI (Paul Scherrer Institute, Switzerland)and TRIUMF has been adopted to interface withthe GRIFFIN electronics modules. This providesa framework for the interface with the electronicsmodules as well as a high-throughput system forwriting experimental data to disk storage.

The hardware of the GRIFFIN DAQ system isarranged into three levels. A schematic represen-tation of the system is presented in Figure 1. Thelower level is the digitizer modules, the GRIF-16and GRIF-4G modules, which process the detectorsignals. The middle level contains GRIF-C Slavecollector modules that collect the data from alllower-level digitizers and communicate it to the toplevel. Each GRIF-C Slave module concentrates the16 input data links into a single output data link.At the top level is the GRIF-C Master collectormodule which filters the data from all modules at

the lower level to either reject it or accept it forread-out to the MIDAS frontend. Also associatedwith the top level is the GRIF-Clk Master clockmodule providing the reference clock distributed toall modules through GRIF-Clk Slave modules, aswell as the GRIF-PPG programmable pulse gener-ator module used to output analogue control signalsfor external equipment synchronization.

All modules in the system are single-width, 6UVME (Versa Module Europa) modules and are op-erated in VME64x crates [7]. The upper, P1 VMEconnector is used to provide power to the moduleand for VME communication. Only the GRIF-C Master and the GRIF-PPG modules commu-nicate over the VME communication bus. Thelower, P2 connector is reserved for analogue signalfeedthrough from the rear-transition cage, as dis-cussed in the description of the GRIF-16 module(See Section 3.1).

Data communication between modules is per-formed over high-quality 4-to-1 cables using themini-SAS connector (SFF-8088). These cables pro-vide one bi-directional data path between eachlower-level module and the next level up.

All modules use a single clock distributed at50 MHz from the GRIF-Clk Master module as thereference clock for all Field-Programmable Gate Ar-ray (FPGA) devices and data links. This clocksignal, in addition to a synchronization signal, isprovided to all modules in the system using cableswith e-SATA connectors. The sync signal is usedto indicate to all modules in the system the start ofdata collection and is used to zero all timestampsand counters.

Detailed descriptions of each module in the sys-tem are given in the remainder of this section.

3.1. The GRIF-16 Digitizer for processing signalswith a preamplifier

The GRIF-16 module (shown in Figure 2) is a16-channel, 14-bit, 100 Msamples/s analogue-to-digital converter (ADC) VME-6U module. Theinput signals are processed by four AD9253 quadADCs and the signal processing of all channels isdone in a single Arria-V FPGA. There is also aVITA 57 FMC (FPGA Mezzanine Card) slot [8]to accommodate either additional input amplifiersand ADCs or additional I/O. The GRIF-16 is usedto read the signals from the GRIFFIN HPGe de-tectors, plastic scintillator detectors (if used with apreamplifier), and Si(Li) detectors.

2

Table 1: Typical properties of the detector signals which are processed by the GRIFFIN DAQ system.

Detector Detector Risetime Decay constant Amplitude PolarityName Type (ns) (µs) (V)HPGe+Preamp Semiconductor 300 50 0.1-1 NegativeSi(Li)+Preamp Semiconductor 200 8 0.1-1 NegativeBGO+Preamp Scintillator 400 0.8 0.1-1 PositivePlastic Scintillator 6 0.018 0.1-0.3 NegativePlastic+Preamp Scintillator 100 20 0.1-1 NegativeBC422Q Plastic Scintillator 1 0.006 0.1-0.3 NegativeLaBr3 Scintillator 8 0.06 0.1-1 NegativeDESCANT Scintillator 10 0.06 0.1-10 Negative

Lower Level Top LevelMiddle Level

GRIF-16Charge-sensitive

preamplifier

GRIF-CMaster x86

midas

Storagedisk

StratixIV

Arria Vadc

GRIF-CSlave

StratixIV

MasterFilter

x16

x16 x16 1Gbit/s

GRIF-PPG

VME

x32NIM/TTL

GRIF-ClkMaster

Sync

GRIF-ClkSlave

CSAC

Sync

Clock

x24

x24

CycloneIII

x4NIM/TTL

GRIF-4G

PMT Stratixadc

x4adc Cyclone

IVCycloneIV GX

Figure 1: Schematic layout of the data and clock paths within the GRIFFIN DAQ system.

3

Figure 2: Photograph of the GRIF-16 module.

The digitizer has two alternative input pathswhich are selectable by a physical switch on theprinted-circuit board (PCB); 16 input MCX (minia-ture coaxial) connectors on the front panel, orinputs through a rear-transition card connectedthrough the VME64x P2 connector. The rear-transition card can easily be exchanged to accom-modate different signal amplification/attenuation,as well as a range of input connectors as additionalvertical space is available. In the GRIFFIN appli-cation the rear-transition card is used with 16 SMA(SubMiniature version A) connectors. This has theadditional advantage of removing a large numberof cables from the front of the VME crate whichmakes maintenance of the digitizers much easier.

Two dual-output, 14 bit, 250 Msps digital-to-analogue converters (DAC) provide signals toLEMO connectors located on the front panel.These same LEMO connectors can alternatively beused as NIM inputs. The front panel has a mini-SAS connector for Gigabit data link to the GRIF-Cmodule. There is also a Small Form-factor Plug-gable (SFP) connector for an ethernet connectionto a general network. An eSATA connection isused to input the clock and sync signals from theGRIF-Clk. The GRIF-16 includes two types of non-volatile memory, a Micro SD Flash card slot and aDDR3 128M x 32, 667 MHz DRAM.

The SFP network connection allows for monitor-ing, diagnostics and control independent of the MI-DAS DAQ system. This is achieved through theGRIF-16 running multiple servers simultaneouslywithin a Nios-II embedded processor on the Arria-V FPGA. In the Nios-II the GRIF-16 module runs

the µCOS/II operating system. Within this op-erating system, multiple tasks are created to han-dle MSCB (MIDAS Slow Control Bus), HTTP, andMIDAS communication and control. The MSCBtasks use a customized MSCB protocol library tocontrol the devices and IO on the board, includ-ing the ADCs. There is also a ‘supervisor’ MSCBtask that allows control via the MSCB UDP MI-DAS Slow Control client. The HTTP task uses theopen-source Mongoose Web Server [9], and deliversstatic web content, JSON, and binary blobs. TheMIDAS task uses the Frozen JSON library [10] toparse and send HTTP GET requests to/from a MI-DAS HTTP server, providing a link between theGRIF-16 module and MIDAS. The final task is anetworking stack that implements UDP, TCP/IPand ICMP. This allows the GRIF-16 module to re-spond to pings, use DHCP, and provide the aboveweb services. Further details on the main user in-terface page is given in Section 6.

A MAX V CPLD controller is used to configurethe devices on the module. Firmware is typicallyloaded from non-volatile flash memory on power-upof the card. It can also be loaded to the devices orto the flash memory through a JTAG connector onthe side of the module. In addition, new firmwarefiles can be saved to the flash memory through theethernet connection using a SFTP server runningon the Nios.

The SFP connector can alternatively be used toconnect the GRIF-16 module directly to a MIDASDAQ system to operate the module in a stand-alonemode. Such a mode of operation is suitable for asmall experimental setup with only a small num-ber of channels and avoids the requirement for theGRIF-C modules. When operated in stand-alonemode the GRIF-16 can use an on-board oscillatoras the reference clock which also avoids the require-ment for a GRIF-Clk module.

3.2. The GRIF-4G Digitizer for processing signalswithout a preamplifier

The TIG-4G module was originally designed atthe Universite de Montreal in 2008 to process thesignals from the DEuterated SCintillator Array forNeutron Tagging (DESCANT) [11] detectors in theTIGRESS DAQ system [4]. The TIG-4G is a 4-channel, 12-bit, 1 Gsamples/s ADC VME-6U mod-ule. The 1 Gsamples/s is accomplished by an inter-leaving of two KAD5512P-50 ADCs.

Two mezzanines accommodate two channels eachwith an SMA input connector for each channel.

4

Figure 3: Photograph of the GRIF-4G module. The lowermezzanine card is removed.

These two mezzanines share a common mother-board which accommodates the (original) AlteraStratix FPGA. Each channel uses two interleavedADC chips each with two A/D cores sampling at250 MHz to achieve an overall sampling rate of1 GHz. The signal processing algorithms for thetwo channels of the mezzanine runs on an AlteraCyclone IV E FPGA located on the mezzanine it-self.

The TIG-4G module was modified in 2014 for usein the GRIFFIN DAQ system by the addition of theeSATA clock connector (described in Section 3.4)and a mini-SAS connector with a Cyclone IV GXFPGA to enable communication with the GRIF-Cmodule via Gigabit links. The GRIF-4G (shown inFigure 3) is used to read out the DESCANT andplastic scintillator signals directly from the PMTwithout the use of a preamplifier.

Firmware is loaded from non-volatile memory onpower-up of the card and can be loaded by a JTAGconnector on the carrier card.

3.3. The GRIF-C Data Collector Module

The GRIFFIN Collector (GRIF-C) module(shown in Figure 4) is a VME-6U module with anAltera Stratix IV GX FPGA as the main proces-sor and a dedicated Xilinx Spartan 6 FPGA foreach of the 3 FMC slots. A Micro SD Flash cardslot and DDR3 128M x 32, 667 MHz DRAM mem-ory are provided on the carrier card. In the nor-mal GRIFFIN system the upper and lower FMCslots house a Data FMC card which has a dual-mini-SAS connector cage. These FMC cards receivedata from the digitizer modules. The central FMC

Figure 4: Photograph of the GRIF-C collector module. TheGRIF-C has three FMC slots, the first (centre) is populatedwith a Communication FMC, the second and third housea Data FMC. The third slot is empty in the photograph sothe Xilinx Spartan 6 FPGA for that slot is visible. The mainAltera Strarix IV GX FPGA can be seen at the centre of thecarrier card.

slot houses a Communication FMC which includesan eSATA connector for the input of the referenceclock to the GRIF-C module, a mini-SAS connec-tor for communication of data to another GRIF-Cmodule, and a SFP connector for communicationof data to the MIDAS DAQ system over a networkconnection. The SFP connection also allows moni-toring and control communication with the GRIF-C module through several servers which run on aNios-II embedded processor.

The collector modules are operated in two levelsas shown in Figure 1. The middle level collectorsare connected directly to up to 16 digitizer moduleseach to concentrate the data collected from themand pass it to the GRIF-C Master collector module.The top level collector module is responsible for co-ordination of the experiment by the sequencer (seeSection 4.8), and runs the master filter algorithm(see Section 4.9) to determine which data are writ-ten to disk and which are rejected.

The hardware and firmware of the GRIF-C Mas-ter and GRIF-C Slave modules are identical. AGRIF-C card will act as a Master if it is configuredas such with parameter settings. A GRIF-C Mas-ter is also capable of communicating directly withthe frontend digitizer cards, rather than indirectlythrough a GRIF-C Slave module, in order to op-erate in a two-level system instead of three-levels.These are useful features, especially for construct-ing a smaller setup where only a few digitizer cards

5

Figure 5: Photograph of the GRIF-Clk Clock module. TheSymmetricom Chip-Sized Atomic Clock can be seen at thelower right of the photograph.

are required.

Firmware is typically loaded from non-volatileflash memory on power-up of the card. It can alsobe loaded to the devices or to the flash memorythrough a JTAG connector on the side of the mod-ule. Alternatively new firmware files can be savedto the flash memory through a SFTP server runningon the Nios-II through the ethernet connection.

Although not yet pursued in GRIFFIN, the FMCslots on the GRIF-C module are designed to also ac-commodate input amplifiers and ADCs in a similarmanner to the GRIF-16 (described in Section 3.1).

3.4. The GRIF-Clk Clock Module

A network of GRIF-Clk clock modules (shown inFigure 5) generate and distribute the master clockand synchronization signals for the entire GRIFFINDAQ system. A single GRIF-Clk Master modulehouses a Symmetricom Model SA.45s Chip-SizedAtomic Clock (CSAC) which produces a precision10 MHz reference signal. A 50 MHz master clocksignal derived from this reference is then fanned-outthrough GRIF-Clk Slave modules to all collectorsand digitizers in the system. Each GRIF-Clk mod-ule has 24 outputs on six 4-to-1 mini-SAS to eSATAcables. There can be 24 digitizers per GRIF-ClkSlave and 24 GRIF-Clk Slaves per GRIF-Clk Mas-ter.

In addition to the reference clock, the GRIF-Clkmodule distributes a sync signal which is used toindicate the start of data collection to all modulesin the system and is used to zero timestamps and

counters. The sync signal is generated by the se-quencer code running in the GRIF-C Master whichhas ultimate experiment control. The signal is thenoutput from the GRIF-PPG module (controlled bythe GRIF-C Master via VME, see Section 3.5) andinput to the GRIF-Clk Master. The GRIF-ClkMaster distributes both the clock and sync signalsto all GRIF-Clk Slave modules which then pass itto the collector and digitizer modules. When theGRIF-Clk module is operated in slave mode the in-put signals are simply fanned-out to the moduleoutput connectors, there are no additional clockcleaners or manipulation of the signal. As all ca-ble lengths and hardware are identical there is verylittle time difference (clock skew) between the sig-nals presented to the collector and digitizer mod-ules. The clock skew was measured to be <700 psand the skew in the sync signal is <400 ps. Thetiming jitter of this distributed clock at the inputto the digitizer module was found to be <16 ps.

3.5. The GRIF-PPG Programable-Pulse GeneratorModule

The GRIFFIN Programmable Pulse Generator(GRIF-PPG) module (shown in Figure 6) generatesNIM and TTL logic signals to be used as controlsignals for equipment such as the Moving-Tape col-lector. The front panel accommodates 32 LEMOoutputs on 16 dual-LEMO connectors, each withan individual switch to select NIM or TTL. Thereare an additional 4 LEMO inputs, again on dual-LEMO connectors at the top of the card which arenot currently utilized in the GRIFFIN DAQ setup.

The cycling of the experiment (beam-on, beam-off, tape move and operation of the electrostaticbeam kicker etc) is controlled by the sequencerfirmware (See section 4.8) in the GRIF-C Mastermodule. The GRIF-PPG module includes a Cy-clone III FPGA which is more than capable of run-ning the sequencer code directly as has been done inother experimental setups. However in the GRIF-FIN system the GRIF-PPG module is used effec-tively as an output register. When the desiredoutput pattern changes in the GRIF-C Master se-quencer this is communicated to the GRIF-PPGmodule by a VME command and immediately pre-sented on the LEMO outputs. The latency betweenthe change in the sequencer and the LEMO outputis on the order of a few microseconds which is neg-ligible with respect to the slow equipment it is usedto control in the GRIFFIN setup.

6

Figure 6: Photograph of the GRIF-PPG ProgrammablePulse Generator module.

4. Signal Processing

The analogue input signal for each channel ofthe digitizer undergoes amplification and filteringbefore being converted to a digital sample by anAnalogue-to-Digital Converter (ADC). A series ofreal-time signal processing algorithms in firmwareconstantly process the digitized data. The outputof these algorithms are recorded when a physicsevent is identified in that channel by the hit de-tection algorithm. The details of these signal pro-cessing algorithms as implemented in the GRIF-16digitizer are described in the following Sections, 4.1to 4.7. The equivalent algorithms in the GRIF-4Gare similar in their working principles. Sections 4.8and 4.9 discuss the operation of additional firmwarealgorithms running in the GRIF-C Master module.

In all cases the parameters of the signal process-ing algorithms can be easily changed through theuser interface as described in section 6. Typicalvalues for the parameters are shown in Table 2.

4.1. Hit Detection

The hit detection algorithm identifies a physicsevent in the detector element connected to the chan-nel and initiates data read-out of the other signalprocessing algorithms. In many cases it is desir-able to be able to identify very low-energy eventsin the face of various background noise fluctuationsof a baseline. Therefore some form of filtering oraveraging must be applied in order to avoid falsenoise triggers. The performance of a number of fil-ter algorithms was investigated both in simulationand on real detector signals. A simple averaging

algorithm was found to be the most effective and isimplemented as a simple version of the pulse-heightevaluation algorithm described in Section 4.2 butrunning very different parameter values as shownin Table 2. The method is the same as the typicalmoving-window deconvolution technique [12–14].

The hit detection is implemented as a set of threeFinite Impulse Response (FIR) digital filters,

AHn = vn − v(n−TH

dif ) (1a)

BHn =

1

THdec

THdif∑i=1

AH(n−i) (1b)

CHn =

1

THint

THint−1∑i=0

AH(n−i) +BH

(n−i) (1c)

where vn is the digitized ADC sample at time nand the constant parameters TH

dif , THdec and TH

int

are the differentiation window width, preamplifierdecay constant and the integration time. A hit isdetected when the value of CH

n is above a thresholdvalue set by the user. An example of the result ofthis algorithm is shown in panel b of Figure 7. Thesample at which this hit is detected is used as thetimestamp value for the event and is equivalent toleading-edge timing. The timestamp value is thetime-zero used as a reference for the other signalprocessing algorithms.

The typical differentiation and integration peri-ods for the hit detection of HPGe signals as shownin Table 2 are 320 and 80 ns respectively which al-lows a threshold of ∼ 5keV (See Section 7.1). Theminimum time difference between hits for them tobe distinguished is one sample longer than the dif-ferentiation time, TH

dif plus the risetime of the sig-nal.

Unfortunately the risetime of HPGe pulses is notconstant. A consequence of this is that the timethe hit detection pulse remains above the thresh-old value is both energy and risetime dependent.In the case of the GRIFFIN HPGe signals from a152Eu source it is found that the overall averagerisetime, measured between 10 and 90% of the fullamplitude, for all energies is 160±50 ns. In the caseof 121 keV pulses the risetime is 210±80

20 ns and for1408 keV pulses it is 150±60

20 ns. At each energythe distribution of risetimes does not have a gaus-sian shape and displays a significant tailing on thelonger-risetime side. In order to accurately knowthe time during which triggers can be accepted a

7

Table 2: Typical values of the parameters controlling the signal processing algorithms in the GRIF-16 module suitable forvarious detector signal types.

Signal Processing Parameter HPGe Plastic ScintillatorAlgorithm + Preamp

Hit detection THdif Differentiation length (ns) 320 320

THint Integration length (ns) 80 80

THdec Decay constant (µs) 52.5 14.0

THDT Imposed fixed deadtime (µs) 1.2 0.3

Pulse-height TEdif Differentiation length (µs) 8.0 6.0

Evaluation TEint Integration length (µs) 7.0 4.0

TEdel Delay before integration (ns) 700 1000

TEdec Decay constant (µs) 52.5 14.0

TEBLR Baseline restore speed (adc units/ns) 0.8 0.8

CFD timing TTdif Differentiation length (ns) 320 320

TTint Integration length (ns) 10 10

TTdel CFD delay length (ns) 30 240

FT CFD scale factor 0.125 0.125

fixed deadtime period, THDT , that is much longer

than the THdif plus the longest risetime time can be

imposed on the hit detection algorithm. An accu-rate knowledge of the deadtime is essential for theconsiderations discussed in Sections 4.5 and 7.5 ondeadtime-corrections and high-rate performance re-spectively.

4.2. Pulse-Height Evaluation

The pulse-height of the detector signal is usu-ally equivalent to the energy deposited in the de-tector element. The pulse-height evaluation algo-rithm transforms the digitized signal into a trape-zoidal pulse from which the pulse-height of the sig-nal can be extracted. The method here is a slightlymodified version of the usual moving-window de-convolution technique [12–14] and includes a cor-rection for any slow baseline-shift which is essentialfor good energy resolution at high counting rates.The method is implemented as a set of four FIR

digital filters,

AEn = vn − v(n−TE

dif ) (2a)

BEn =

1

TEdec

TEdif∑i=1

AE(n−i) (2b)

CEn = CE

(n−1) − TEBLR sgn(AE

(n−1) +BE(n−1)) (2c)

DEn =

1

TEint

TEint−1∑i=0

AE(n−i) +BE

(n−i) + CE(n−i) (2d)

where vn is the digitized ADC sample at timen and the constant parameters TE

dif , TEdec, TE

int

and TEBLR are the differentiation window width,

preamplifier decay constant, integration time andbaseline-restore speed respectively. Typical valuesfor these parameters are shown in Table 2.

The filters are applied sequentially to the dig-itized preamplifier signal (Figure 7a), beginningwith the difference filter given by Equation 2a. Thisremoves the DC offset, effectively shifting the base-line of the signal to zero. After applying this filterthe signal still has a negative pole associated withthe decay constant, TE

dec, of the preamplifier signal(Figure 7c). To compensate for the decaying base-

8

s)µTime (2− 0 2 4 6 8 10 12 14

AD

C u

nits

200−

0

200

400

600

800

1000

1200

1400

(a) ADC sample

s)µTime (2− 0 2 4 6 8 10 12 14

AD

C u

nits

200−

0

200

400

600

800

1000

1200

1400

(b) Hit detection

s)µTime (2− 0 2 4 6 8 10 12 14

AD

C u

nits

200−

0

200

400

600

800

1000

1200

1400

(c) Differentiated signal

s)µTime (2− 0 2 4 6 8 10 12 14

Inte

gra

ted A

DC

units

200−

0

200

400

600

800

1000

1200

1400

(d) Pulse­height evaluation

Figure 7: A digitized HPGe preamplifier waveform (a), withthe result of the hit detection algorithm (b) and the pulse-height evaluation algorithm (d). Panel c shows the differen-tiated signal (Equation 2b) at the intermediate stage of thepulse-height evaluation algorithm. The shaded red regionindicates from which times following the hit detection, thefinal pulse-height evaluation result can be taken from. Seetext for details.

line, Eq. 2b is applied to the resulting waveform tocalculate the deficit associated with the decay. Thedeficit is added to the result of Equation 2a givingthe trapezoidal signal, shown in Figure 7(d). Therising part of the signal has a shape which reflectsthe rise of the preamplifier signal and the fallingpart is its mirror. In the ideal case the preampli-fier will have a single exponential component (thedecay constant TE

dec) and where this exactly knownthe baseline of the corrected signal would lie flatalong the horizontal axis. Other noise contributionssuch as 60 Hz noise pick-up would still be presentthough as fluctuations around the baseline. Furthercompensation to the baseline shift is achieved usingEquation 2c. This is similar to methods describedin Ref. [15] but implemented here in firmware as areal-time algorithm.

Equation 2d is a low-pass filter which integratesover a number of samples, given by the parameterTEint, to remove the remaining high-frequency noise

from the top of the signal. It is necessary to pro-vide this integral value in the data on disk as it candeviate from the nominal value during the process-ing of pile-up events (See Section 4.4). The pulseheight, usually proportional to energy, can then bedetermined by dividing the integral returned fromEquation 2d by the integration length, TE

int. (Oftena fraction of the integration length is used in orderto maintain good channel dispersion in the energyspectrum.) The integration length is the equiva-lent of the shaping time employed by a traditionalanalogue spectroscopy amplifier [12–14]. The inte-gration length TE

int must be less than the differen-tiation time TE

dif . The pulse-height value is readout at the time when the sample number i is equalto the time-zero as given by the hit detection plusTEdel + TE

int. The delay TEdel is necessary to ensure

the full collection of charge has happened before theintegration begins.

4.3. Timing

In addition to the timestamp value provided bythe hit detection algorithm in Section 4.1, a tim-ing algorithm from a digital implementation ofa Constant-Fraction Discriminator (CFD) is pro-vided. This is essential to compensate for theamplitude-dependent time-walk which is inherentto detectors such as HPGe. The time-walk effect ismost significant for low-energy signals and can beas large as 300 ns for these large-volume HPGe crys-tals when a leading-edge type algorithm is applied.

9

The constant fraction is evaluated as,

CTFn =CT

n

FT− CT

(n−TTdel)

(3a)

where,

CTn = vn − v(n−TT

dif ), (3b)

TTdel is the CFD delay time, FT is the CFD scale

factor and TTdif is the differentiation length which

must be greater than the risetime of the pulse. Thezero-crossing point is when CTFn = 0 and is takenas the result of the timing algorithm.

4.4. Summing and Pile-up

Signal pile-up occurs when more than one energydeposition from different physics events is presentin a detector element during the processing timeof the initial interaction. Summing occurs whenthese two energy depositions occur so close in timethat they cannot be distinguished. There are twodistinct types of summing;

1. True-coincidence summing occurs when twocoincident gamma rays from the same physicsevent are detected in the same detector ele-ment. This is dependent on the details of thenuclear decay and the geometry of the detectorsystem, but is independent of the event rate.It will not be discussed further here.

2. Random-coincidence summing occurs whengamma rays from separate physics events aredetected in the same detector elements withan unresolvable time difference. The observedenergy is equal to the sum of the two energydepositions and therefore affects the apparentefficiency by removing counts from the individ-ual photopeaks and adding counts to the sumphotopeak.

The term summing will refer to random coincidencesumming in the remainder of this document. It isan important rate-dependent effect that must betaken into account in the GRIFFIN data acquisitionsystem at the same time as considering pile-up.

Figure 8 shows the different relative timing sce-narios of hit detection events. The probability ofsumming is dependent on the imposed fixed dead-time, TH

DT , of the hit detection algorithm. Theprobability of pile-up is dependent on the length ofthe differentiation window, TE

dif , of the pulse-height

algorithm which is normally 1 µs longer than theintegration period, TE

int, and on the imposed fixeddeadtime, TH

DT , of the hit detection algorithm.It is a primary goal of the GRIFFIN DAQ system

to operate the HPGe detectors at a counting rateup to 50 kHz per crystal. As the probability of pile-up increases with counting rate it is essential thatas many events as possible are recovered so thatthe high efficiency of the detectors is not lost. Theway in which instances of pile-up is handled in theGRIF-16 firmware is described here.

If the time between hit detections is greater thanthe differentiation period of the pulse-height algo-rithm, TE

dif , then there is no pile-up. The origi-nal hit detection and subsequent hit detection aretreated in the normal way as separate events.

If there are two or more hit detections within thedifferentiation period, TE

dif , following the originalhit detection (Figure 9) then these multiple hitswill be handled as pile-up events. The minimumtime difference between hits for them to be distin-guished is one sample longer than the hit detectionimposed fixed deadtime. Each hit is processed sep-arately and generates a new event packet that willbe written to disk. These events are labelled aspile-up events with a flag in the data which allowsthem to be treated separately in the offline analysis,if desirable.

The longest integration period possible for eachhit will be used on the non-piled-up region of thesignal. This will be shorter than the nominalintegration period specified in the parameter forthe pulse-height algorithm. The integration periodused in each case, which is necessary for determin-ing the pulse-height value for each interaction is in-cluded in the event (regardless of whether the eventis pile-up or not). An improvement in the energyresolution of both hits can be made if in additionto the individual integration regions of both hits,the integral of the summed region is also recordedand a minimization performed to extract the twoindividual pulse-heights.

Each additional hit extends the differentiationperiod of the original hit. There is a limitation tothe maximum number of hit detections within theoriginal differentiation period for which reasonableenergy resolution can be achieved. All events areprocessed but events in which an integration periodof less than 1 µs was applied will have noticeablypoorer energy resolution (See Section 7.2). Thislimitation is typically reached when more than 3interactions occur within the differentiation period

10

Hit 1No Hit

Hit 1 processing timeNo Hit

Hit 2

Hit 2 processing time

Hit 2Summing:

Pile-up:

Hit 3

Hit 3 processing time

-T difE -TDT

H T0 T DTH T dif

E

AdditionalPile-up:

Figure 8: Schematic diagram of hit detection scenarios that are processed as summing or as pile-up.

of the original hit.The methodology and equations for calculating

the probability of the various summing and pile-up scenarios in the GRIFFIN DAQ system are de-scribed in detail in Appendix A. Based on theseprobabilities, it can be seen in Figure 10 that theprobability of summing and pile-up increases withthe counting rate of the detector element. At arate of 50 kHz with TH

DT = 1.2µs and TEdif = 8µs

that rejecting all pile-up will result in only 46.4% ofevents being collected. The GRIFFIN DAQ systemapproach to pile-up recovery will recover 80.7% ofevents with 10.7% lost to > 3 pile-ups and 8.6%to summing. Even higher retention of relative ef-ficiency can be achieved with short differentiationperiods but at a reduction in energy resolution.

4.5. Deadtime

Deadtime is the total period of time during whichhit detections cannot be processed even if they arepresent. In the GRIFFIN DAQ system deadtimeis applicable on a single channel basis and thereis no overall global deadtime. System wide effectssuch as data loss are possible but should be treatedseparately from deadtime as the individual chan-nels are still accepting and processing hits. Thetotal deadtime period for a data collection periodis equal to the imposed fixed deadtime of the hitdetection algorithm multiplied by the total numberof hit detections during that data-collection period,plus any additional deadtime from hits not beingaccepted. Hits can be rejected for instance if thememory buffer on the GRIF-16 module is full. Thedeadtime period since the previous accepted hit is

recorded in the 14-bit deadtime word of each event.It has a maximum value of 163.83 µs.

4.6. Event Traceability

Events are generated for each channel in thelower-level digitizers (GRIF-16 or GRIF-4G). It ispossible that events will be lost by memory buffersbecoming full or link communication errors beforethey are written to the disk file. This event losscan be identified and accounted for by examiningseveral counters provided in the GRIFFIN data.

The channel hit detection counter is a counterthat is incremented for each individual channel eachtime a hit detection is identified by the hit detectionalgorithm. A subsequent event on disk from thatchannel will have a channel hit detection countervalue that is one greater than the previous eventunless an event was lost due to some form of dataloss. If the channel hit detection counter indicatesthat an event was lost then it can be accounted foras effective deadtime of that channel because thisgenerates a period of time, equal to the differenti-ation period TH

dif , plus the signal risetime duringwhich hit detections effectively could not be pro-cessed. A second counter called the accepted chan-nel hit counter is also generated in the lower-leveldigitizers for each individual channel. The acceptedchannel hit counter is only incremented when anevent leaves the final memory buffer on the digi-tizer. Using both the channel hit detection counterand accepted channel hit counter together can de-termine if any event loss has occurred in the lower-level module or in another module of the system.

11

s)µTime (0 5 10 15 20 25 30

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s)µTime (0 5 10 15 20 25 30

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Figure 9: Same as Figure 7 but showing three interactions.The first one is a single event, the second two are consideredas a pile-up event with two interactions occurring within the6.8 µs differentiation period. The integration length used inthis pile-up example is TE

int=2 µs. The shaded red regionindicates from which times following each hit detection thefinal pulse-height evaluation result can be taken.

Count rate (kHz)

0 10 20 30 40 50 60 70

Pro

bab

ility

of S

um

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g

0.00

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ile­u

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0.1

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(b)sµ8.0

sµ6.0

sµ4.0

Figure 10: Calculated probabilities for the occurrence of (a)summing and (b) pile-up events as a function of countingrate for different values of the imposed fixed deadtime of thehit detection and differentiation period of the pulse-heightalgorithms respectively.

12

An additional counter, the network packetcounter, is added at the final memory buffer ofthe GRIF-C Master just before the event leaves theGRIFFIN electronics. The network packet countershould increment by one each time data is com-municated between the GRIFFIN electronics andMIDAS. If one is missing it can be attributed todata loss over the network or in MIDAS.

Using both the accepted channel hit counter andnetwork packet counter it is possible to identify ifevent loss happened in the GRIFFIN electronics orin the network transfer and MIDAS. Any event losscan be accounted for in the offline analysis of GRIF-FIN data.

4.7. Scalers

There are two types of scalers generated by theGRIF-16 digitizers; monitoring scalers and fixed-deadtime scalers.

Scalers for monitoring the counting rates of eachchannel are generated in the GRIF-16 and commu-nicated to the MIDAS system for operational moni-toring purposes only and are not written to the diskfile. These rates scalers reflect all identified hit de-tections from the hit detection algorithm for eachchannel.

Every channel has a set of four fixed-deadtimescalers that are read out at a regular period of timewhich is a user selectable parameter. Each hit de-tection from the hit detection algorithm is passedto the fixed-deadtime scalers. Each hit detectionincrements the scaler by one if the scaler is live.A different fixed deadtime is imposed on each ofthe scalers and subsequent hit detections are notcounted if they are received within this fixed periodfollowing a hit detection. The fixed deadtimes are0, 1, 10 and 100 microseconds. The 0µs scaler willhave an actual deadtime equal to the fixed deadtimeperiod of the hit detection algorithm.

4.8. The Sequencer

GRIFFIN experiments are usually performed ina cycling mode. When the radioactive beam is de-livered it is implanted into the tape of a MovingTape collector at the central focus of the GRIF-FIN detectors. When the tape moves, the sampleis transported behind a wall of lead shielding andaway from sight of the detectors. A typical cycleinvolves a tape movement, background data collec-tion, data collection while the radioactive beam isbeing delivered, and finally a period of data collec-tion with the radioactive beam blocked. Blocking

of the beam is achieved by an electrostatic kicker.The relative duration of each stage within the cyclecan vary between tens of milliseconds and tens ofminutes in different experiments, depending on thehalf-lives and relative beam intensities of the iso-topes involved, as well as the goal of the measure-ment. Control of this cycling mode is performedby the sequencer firmware running in the GRIF-CMaster module.

A series of parameters are loaded to the sequencerat the beginning of data collection. The parame-ters represent the bit pattern of logic signals to beoutput on the front-panel LEMO connectors of theGRIF-PPG during each part of the cycle, and theduration for each pattern to be output. The param-eters for a typical measurement cycle are shown inTable 3. The sequencer communicates the desiredbit pattern to the GRIF-PPG module through aVME communication. After the specified durationfor that pattern, the next pattern is communicatedto the GRIF-PPG module. This continues until theend of the data collection.

The duration is specified in microseconds so the32-bit parameter can accommodate a maximum du-ration of 71.583 mins. Longer times can be con-structed by repeating the same pattern in sequen-tial parameters if desired.

The GRIF-C Master produces an event that iswritten to disk each time the sequencer patternchanges. This event includes the timestamp atwhich the change occurs, the previous pattern inthe sequencer, the new pattern in the sequencer andthe pattern read back from the GRIF-PPG modulewhich should match the new pattern. These specialPPG events in the disk file can be used to recon-struct the cycles during offline analysis of the data.

Although the bit patterns are 16-bits, there areonly actually two logic signals required to operatea typical GRIFFIN cycle; one for the electrostatickicker that controls beam delivery, and one to initi-ate a movement of the Moving Tape collector. Thebackground collection and the period of data collec-tion with the radioactive beam blocked are in factan identical hardware situation. However, using adifferent bit pattern to indicate these different partsof the cycle is very useful in the offline data analysis.In the future, more complex hardware setups couldbe controlled with the other logic signals, for exam-ple lasers on/off for polarization measurements ora vacuum valve opened/closed for gas-handling aspart of the measurement cycle. An example of suchan experimental setup is that which would be re-

13

Table 3: Parameters to operate typical measurement cycles of GRIFFIN, controlled by the sequencer firmware and providinganalogue logic signals from the GRIF-PPG module.

Operation Bit-pattern Pattern duration (s)Isotope: 32Na 62Ga 26Na 46K 152EuHalf life: 13.2(4) ms 116.121(21) ms 1.07128(25) s 105(10) s Offline source

Move Tape 0xC008 1 1.5 1 1.5 -Background 0xC002 - 2 0.5 10 -Beam on 0xC001 0.2 10 3 150 -Beam off 0xC004 1 2 15 300 ∞

quired for an electric dipole moment search in radonisotopes at TRIUMF-ISAC [16].

4.9. The Master Filter

The master filter consists of a series of logicmodules built in the firmware of the GRIF-CMaster and executed in real time. All eventscollected in the digitizers are presented to themaster filter where they are either rejected oraccepted and written to disk. Figure 11 gives anoverview of the flow of events through the masterfilter. The function of each component is describedhere.

Input Buffer:The input buffer receives events from all GRIF-CSlave modules and must be capable of holding allevents collected during the processing time of themaster filter algorithm. An unfiltered data path canbe used to bypass completely the other componentsof the master filter. This was especially usefulin the development and testing of the system.The filtered data path proceeds through all othercomponents of the master filter. The majority ofthe event data is held at the input buffer whilethe detector type, address and CFD-correctedtimestamp are processed by the algorithms inorder to determine if the event should be acceptedor rejected. If an event is rejected then it is deletedfrom the input buffer. If an event is accepted thenit proceeds to the output buffer for communicationto disk storage.

Time-ordering:The algorithms in the components that followdepend on the events being in sequential timeorder. There can be some latency of eventsoriginating from digitizers connected to differentGRIF-C Slaves. Therefore the first stage of the

master filter is to time-order the incoming eventsbased on the CFD-corrected timestamp providedby the hit detection signal processing algorithm.

BGO Suppression:Events which are identified with the detector typeof HPGe are scrutinized for the presence of eventsfrom the associated BGO suppression shields. Themapping of BGO suppression shield channels toHPGe channels is controlled by parameters whichare loaded to the GRIF-C Master at the start ofeach data collection period. If an associated BGOevent is present within a user-defined coincidencewindow then the HPGe and BGO events will berejected and will not be processed by the followingcomponents of the master filter.

This part of the master filter can optionally bedisabled to ensure all HPGe and BGO events arewritten to disk where Compton-suppression can beperformed offline.

Detector Type Selection:A parameter is used to determine which detec-tor types can proceed to be considered by thedownscaling and coincidence condition algorithms.There are provisions for up to 14 different detectortypes. Any events with detector types that are notenabled are rejected at this point.

Downscaled singles:The ability to record Downscaled singles datais essential in high counting rate situations inorder to extract absolute branching ratios withoutoverwhelming the data rate with singles data.Downscaled singles events are not presented to theCoincidence Filtering algorithm but are passeddirectly to the Output Buffer for communicationto disk storage. As an example for DownscaledBeta events with a Downscale factor of 100, the

14

Outputbuffer

Inputbuffer Unfiltered

Timeordering

of allfragments

BGOSuppression

Filter byDetector

Type

Downscalingof singles

Coincidenceconditions

Downscaledsingles

FilteredReject Reject

Reject

Reject

Figure 11: Schematic layout of the master filter algorithm in the GRIF-C Master.

algorithm would accept one in every 100 betaevents presented to it. The one accepted eventis passed to the Output Buffer and the other 99are rejected. Using the 16-bit parameter size theDownscale factor can have a value between 2 and65,535.

Coincidence Filter:A series of parameters define the required multiplic-ity of various detector types which must be presentwithin a user-defined coincidence window in orderto pass the Coincidence Filter. Up to 14 differ-ent Coincidence Filter conditions can be set at onetime. Each Coincidence Filter condition can involveone or more detector types. As an example, HPGedoubles or a β-γ-neutron coincidence use one andthree detector types respectively. Singles events arealso included as Coincidence Filter conditions withmultiplicity 1 for that detector type. In addition,there are special detector types of “Clover” and“Suppressed Clover” that can be used in Coinci-dence Filter conditions.

The event CFD-corrected timestamps are used toinspect the relative time difference between events.Once a Coincidence Filter condition is passed allevents in the coincidence window at that time areflagged as passing the Coincidence Filter and aresubsequently passed to the Output Buffer. Forthis reason it is essential to control which detectortypes are presented to the Coincidence Filter withthe detector type Selection algorithm to avoid alarge data rate from a detector type that is notdesired. However this behavior does ensure thatif a gamma-beta event occurs then any additionalcoincident neutron events will pass the master filter

if DESCANT is enabled. Each event is labeledwith which master filter condition or conditionshave been passed, and a counter representing howmany events have passed the master filter since thebeginning of the data collection period.

Output Buffer:All data that is passed to the Output Buffer is com-municated over the network to the backend com-puter in order to be written to storage disk.

5. Structure of the Data

The data from the GRIFFIN DAQ system is pro-cessed by the MIDAS data acquisition system [6]which provides a framework for writing the experi-mental data to disk storage. The format of the datafollows the standard MIDAS approach of a series of32-bit words wrapped by standard MIDAS headerand trailer words. Table 4 lists all the informationcontained in each 352-bit basic GRIF-16 event con-sisting of eleven 32-bit words. The fixed-value bitsused as masks to identify the purpose of data wordsis not included in the size value but is in the 352-bit total. If waveform samples are included in thereadout then this event size is larger as there areadditional words. Also if more than one filter con-dition has been satisfied the event size is increasedwith an additional word for each filter conditionpassed. Multiple GRIF-16 events (typically ∼1000)are contained within each MIDAS event on disk.

The GRIF-4G module can produce some addi-tional information if processing the DESCANT de-tector type. These are not discussed in detail here

15

but include the results of several pulse-shape anal-ysis algorithms used to distinguish neutron andgamma events in the deuterated scintillator [17].

6. User Interface

A user-friendly interface has been developed tointeract with the GRIFFIN DAQ system in or-der to make regular tasks such as rate-monitoringor parameter changes straight-forward to complete.The user interface is integrated into the MIDASDAQ system in order to read and write parametersfrom a single, centralized location called the OnlineDataBase (ODB). At the beginning of a data collec-tion period the parameters are read from the ODBand written to all electronics modules to ensure syn-chronized values. A copy of the entire ODB is writ-ten to the disk file at the start and end of each datacollection period for reference during analysis. Alluser interface pages are provided in web browsersand various pages are provided from two differentservers. The pages are constructed primarily usingJavascript. The mhttpd server of MIDAS providesa general Dashboard interface page which includescontrol of the main parameters of the GRIFFINfacility such as cycle control or master filter logic(shown in Figure 12). In addition, each GRIF-16digitizer runs a separate server to provide an in-terface page for that individual digitizer. When aparameter is changed from a page running from anindividual digitizer the value is immediately syn-chronized in the ODB and percolated to all otherinterface pages.

A screenshot of an example GRIF-16 digitizerUser Interface showing the rates, scalers and anyerror reporting for the 16 channels of the moduleis shown in Figure 13. A screenshot of an exampleGRIF-16 digitizer User Interface for a single chan-nel is shown in Figure 14. The waveforms updatein real time similar to a digital oscilloscope. Themenus on the right allow the user to change pa-rameters of the signal processing algorithms duringsetup mode and when data is not being collected.A software lock prevents parameters being changedduring data collection as this would create difficultanalysis situations.

7. Performance of the System

The majority of the experiments performed todate with GRIFFIN have been focused on mea-surements relevant to nuclear structure and nuclear

Figure 12: Screenshot of the Dashboard User Interface show-ing the control page of the master filter.

Figure 13: Screenshot of an example GRIF-16 digitizer UserInterface showing the rates, scalers and any error reportingfor the 16 channels of the module.

16

Table 4: List of the information provided in a data event written to disk. BOR stands for Beginning Of Run, representing thestart of the data collection period.

Data Size1 Description(bits)

Module type 3 Module type (GRIF-16 etc) that generated this eventAddress 16 Unique identifier for the channel that produced this dataDetector type 4 Identifies the detector type (HPGe, BGO etc)Network packet counter2 28 Total network packets generated since last module initializationFilter condition counter3 31 Total number of events passed by filter since BORFilter patterns 14 Reports which filter patterns this event passedTimestamp 42 Elapsed time since the BORChannel hit detection counter 28 Total number of hits in this channel since BORChannel accepted hit counter 14 Total hits in this channel while it was live since BORPile-up type 5 Reports the number of hits during this eventIntegration length 14 Integration length applied in the pulse-height algorithmPulse-height 28 Result of the pulse-height algorithmCFD 22 Result of the timing algorithmDeadtime 14 The duration of the deadtime preceding this eventWaveform N*14 Raw ADC data (present if waveform readout is enabled)Total size of standard event without waveforms = 32-bit × 11 words = 352 bits

1 This size value only includes the data bits. Fixed-value bits of the 32-bit words used as masks to identifythe purpose of data words is not included.2 Only has a value for the first GRIFFIN event in a network packet.3 May appear multiple times in one event.

17

Figure 14: Screenshot of an example GRIF-16 digitizer UserInterface for a single channel. The waveforms update in realtime similar to a digital oscilloscope. The menus on the rightallow the user to change parameters of the signal processingalgorithms.

astrophysics investigations. In such measurementsthe performance features of primary relevance aredetection efficiency and spectral quality. A maindesign goals of the GRIFFIN DAQ system was toensure these features up to high counting rates inorder to collect ultra-high statistics datasets andsearch for very low-intensity decay branches. Theperformance of the GRIFFIN DAQ system is pre-sented here.

7.1. Low-Energy Thresholds

The hit detection algorithm in the GRIF-16 (Sec-tion 4.1) successfully triggers on 5 keV equivalentsimulated pulses injected into the ADC data of areal detector baseline. When examining real GRIF-FIN HPGe detector signals, as can be seen in Fig-ure 15, the germanium K x-ray peak at 9.9 keV canclearly be identified which is the result of photonsmoving between crystals inside the HPGe clovercrystal housing. These events can be used in theadd-back method to improve the full-photopeak de-tection efficiency [3]. However, with a thickness of1.5 mm the aluminum housing around each cloverdetector heavily attenuates photons of this energyfrom reaching the crystals from outside. Thereforethe DAQ is capable of triggering at a lower energythan the HPGe detectors are expected to observefrom external sources.

7.2. Energy Resolution

The Full-Width at Half Maximum (FWHM) ofthe full-energy photopeak for the 122 keV and

Energy (keV)0 20 40 60 80 100 120 140

Co

un

ts p

er

0.2

4 k

eV

210

310

410

510

121 keVSm X rays

Ge X rays

Escape peak

Figure 15: HPGe energy spectrum of a 152Eu source col-lected with a GRIF-16 digitizer showing the low-energy re-gion. The energy resolution of the 122 keV peak is 1.07 keV.The escape peak at 30 keV results when an incident Sm Xray is detected but the Ge X ray escapes the crystal. TheGe X ray peak is visible at 9.9 keV.

1332 keV gamma rays from 152Eu and 60Co de-tected in a single GRIFFIN HPGe crystal are typ-ically 1.07(1) and 1.87(1) keV respectively whenmeasured using a GRIF-16 digitizer at low countingrate.

The energy resolution as a function of the inte-gration time, TE

int, is shown in Figure 16. In eachcase the differentiation time, TE

dif , was 1 µs longer

than TEint. The energy resolution improves with

increasing integration time and is essentially con-stant above 6 µs. The reduction in performancewith shortening integration time is a limiting fac-tor in the energy resolution of pile-up events at highcounting rates, as discussed in Sections 4.4 and 7.4.

The linearity of the energy response in the GRIF-16 digitizer has been measured in the energy rangefrom 122 to 3253 keV using radioactive sources of152Eu and 56Co. The linearity in gain was foundto be better than 0.3 keV in this energy range incomparison to 0.2 keV measured for the GRIFFINHPGe detectors with a TIG-10 digitizer [3].

When counting at high rates the DC offset of thebaseline of a HPGe signal will vary considerably asseen in Figure 9a. This means different regions ofthe ADC will be used to measure the same energyfor different hits. The linearity was also investi-gated for different regions of the ADC by exam-ining the energy response to the 59.5 keV gammaray from a 241Am source at <1kHz and adjustingthe DC offset manually using the input DAQ of theGRIF-16 module. The linearity of the response wasalso found to be better than 0.3 keV over the full

18

s)µIntegration Length (0 2 4 6 8 10

FW

HM

(ke

V)

1.7

1.8

1.9

2.0

2.1

2.2

2.3

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2.5

2.6

Figure 16: FWHM resolution (keV) of the 1332 keV gammaray from 60Co plotted as a function of the integration length(µs) used in the pulse-height evaluation algorithm. Data arefor a single HPGe crystal counting at low rate (≈ 300 Hz).

ADC range.

7.3. Coincident-Timing Resolution

The result of the timing algorithm is shown inFigure 17 where the time difference between coin-cident gamma-gamma events from a 60Co sourceare processed in the GRIF-16 digitizer. A condi-tion that the crystal multiplicity is equal to twois imposed and the energy required is greater than20 keV. The shape of the distribution is not a Gaus-sian so the usual FWHM cannot be quoted. Thewidth of this coincidence timing peak containing68 % of events is 32(2) ns and 95% of the data iswithin 174(8) ns.

The performance of the timing algorithm is sen-sitive to the values of the Delay, TT

D , and Fraction,FT , parameters. The systematic behavior can beseen in Figure 18. The time difference betweenall events from HPGe signals with energy >20 keVviewing a 60Co source is included in this analysis.

7.4. Spectral Quality at high counting rate

The systematic behavior of various performancemetrics is shown in Figure 19 as a function of in-dividual HPGe crystal counting rate. Ideally thesystem will be able to collect data at high count-ing rates with the same spectral quality as at lowcounting rates. In order to achieve a good spec-tral quality the energy resolution and peak-to-totalratio must remain high as a function of countingrate. The coincident-timing resolution at all rates isimportant for the accurate subtraction of random-coincidence background contributions. In additionthe relative efficiency of the detector system must

Time difference (ns)

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rma

lize

d c

ou

nts

pe

r n

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(95 % events)

Figure 17: Time difference between coincident gamma-gamma events from GRIFFIN HPGe signals processed inthe GRIF-16 digitizer by the timing algorithm. A thresh-old of 20 keV has been applied to both coincident energies.An additional requirement of single interactions (no pile-up)within each HPGe crystal was imposed. At an incident rateof <5 kHz in each crystal, 68% of the coincidence eventshave a time difference less than 32(2) ns and 95% of the co-incidence events are contained within a width of 174(8) ns.

also remain high with increasing rate which is dis-cussed in Section 7.5.

The data for the energy resolution, timing reso-lution and peak-to-total plots were collected usingthe GRIF-16 digitizer and GRIFFIN clovers observ-ing a 60Co source. The crystal counting rate wascontrolled by changing the source-to-detector dis-tance. Note that this also changes the solid anglesubtended by the detector and therefore the proba-bility of true-coincidence summing is changed at thesame time as the counting rate. This does not affectthe performance results obtained for the aforemen-tioned metrics.

Note that in all examples of “all interactions”and “no pile-up” that these conditions are appliedin the offline analysis with all data being recordedto disk by the DAQ system.

The pile-up recovery in the GRIFFIN DAQ sys-tem does come at a cost to energy resolution ascan be seen in Figure 19a in the comparison be-tween single-interaction and pile-up events, but isessential to maintain a high detection efficiency asdiscussed in Section 7.5. There is an increase in en-ergy resolution as a function of counting rate that

19

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Figure 18: The width containing 68 % of the time differencepeak between coincident gamma-gamma events from GRIF-FIN HPGe signals as a function of the Delay (panel a) andFraction (panel b) parameter values used in the timing algo-rithm. The Delay parameter was maintained at a constantvalue (equal to 14) during each Fraction setting in panel b.The time difference between all events with energy >20 keVfrom a 60Co source is included.

is almost linear and following the trend of the pile-up fraction (Figure 10). This increase is in partdue to the unavoidable reduction in the integra-tion period, TE

int, applied during the pulse-heightevaluation of pile-up events. The energy resolutionincreases from 2.0keV at ∼1 kHz to >4 keV above50 kHz. This will obviously reduce the resolvingpower of the spectrometer and limit the ability todetect very weak intensity decays. It may be pos-sible to further improve the energy resolution algo-rithm performance at high counting rates.

One of the primary objectives in high-statisticsexperiments is the construction of level schemesthrough a gamma-gamma coincidence analysis.The resolution of coincidence timing is importantin order to reject false and background coincidentevents from the spectra. Figure 19c shows that theperformance of the timing algorithm remains thesame to count rates of 40 kHz but worsens at higherrates.

The peak-to-total ratio remains approximatelyconstant up to counting rates of 40 kHz (Figure19c) showing that the spectral shape remains verysimilar.

7.5. Relative Efficiency at high counting rate

Figure 10 shows that it is essential to handlepile-up events in an effective way in order to main-tain a good detection efficiency because at count-ing rates of ∼50 kHz around 45% of events pile-upwithin a 6 µs differentiation period. If one simplyrejects pile-up events by considering only single-interaction events then the relative detection effi-ciency is greatly reduced at high counting rates. Inthe GRIFFIN DAQ system however, the majorityof pile-up events are recovered and therefore a highrelative detection efficiency is maintained. Very lit-tle data loss is of course also a requirement whencounting up to 50 kHz per crystal which is equiv-alent to roughly 134 MB per second for 64 HPGecrystals.

Figure 20 shows the relative efficiency as a func-tion of crystal counting rate. In the determinationof the relative efficiency, the probability of true-coincidence summing is an important considerationand therefore the distance of the source must beconsistent for the measurement at each countingrate. In this case a 60Co source was placed at afixed distance from the detector and data collectedfor 3 mins at each counting rate. The counting ratewas controlled by changing the distance of a 137Cs

20

Count rate (kHz)

0 20 40 60 80

Energ

y R

esolu

tion (

keV

)

2

3

4

5

(a)

Count rate (kHz)

10 20 30 40 50

Coin

cid

ent T

imin

g R

esolu

tion (

ns)

20

30

40

50

60

70

80

(b)

Count rate (kHz)

10 20 30 40 50

Peak­t

o­t

ota

l ra

tio

0.10

0.11

0.12

0.13

0.14

0.15

0.16

(c)

all interactions

no pile­up

Figure 19: Energy resolution (a), coincidence-timing resolution (b) and peak-to-total ratios (c) as a function of individualcrystal counting rate collected using the GRIF-16 digitizer and GRIFFIN clovers observing a 60Co source. See text for details.

21

Count rate (kHz)10 15 20 25 30 35 40 45 50

Re

lative

Eff

icie

ncy

0.4

0.5

0.6

0.7

0.8

0.9

1.0

all interactions

no pile­up

Figure 20: Relative efficiency at 1173 keV as a function ofindividual crystal counting rate collected using the GRIF-16 digitizer and GRIFFIN clovers observing a 60Co source.Calculated relative efficiency curves considering all interac-tions and single hits are shown as dotted lines. See text fordetails.

source with respect to the detector. Here the pa-rameters TH

DT = 1.2µs and TEdiff = 8µs. The data

points with solid lines represent the experimentalresults and the dashed lines are the result of theequations discussed in Section 4.4 and AppendixA.

The apparent relative efficiency at higher count-ing rates will be reduced by random-coincidencesumming and by pile-up scenarios that are not de-convolved in the data analysis process.

A comparison of the gamma-ray energy spectrafrom a 60Co source collected at crystal countingrates of 1 and 50 kHz is shown in Figure 21. In eachcase the source-to-detector distance was ∼50 cm.The spectra are normalized by the number of countsin the 1332 keV peak. The upper panel shows onlysingle interactions equivalent to pile-up rejectionwhereas the lower panel shows all interactions, theequivalent of pile-up recovery. In this example, atthe high counting rate the same level of statisticscan be collected in <3% of the data collection pe-riod required at the low counting rate. Good spec-tral quality is seen in both spectra indicating thatthe design goal for high counting rate operation hasbeen achieved.

7.6. Fixed-Deadtime Scalers

The functionality of the fixed-deadtime scalers isdescribed in section 4.7. The fixed deadtimes im-posed on each scaler were measured independentlyusing a variation of the paired-source method in-troduced by A. P. Baerg [18] where one of a pair of

random sources is replaced with a periodic pulse ofknown frequency. Provided that the pulse period isgreater than the non-extending deadtime applied toa given channel, the deadtime may be measured bycomparing the combined counting rate of the sourceand periodic pulse with the rate of the source alone.The measured deadtime τdm is given by

τdm =1

Rs

√1− Rc −Rs

Rp, (4)

where Rs is the random source rate, Rp is the fre-quency of the periodic pulse and Rc is the combinedrate of the source and periodic pulse measured bythe scaler. The measurement was performed as fol-lows. A 9.28 µCi 137Cs source was placed nearthe center of a single hemisphere of the GRIFFINHPGe array. The periodic square-wave output ofan Agilent 33522A arbitrary waveform generatorwas used to produce a logic pulse from an ORTECGG8020 gate generator that was connected to thetest input connector of 9 HPGe crystal in the samehemisphere. As the Pulser signal was delivered di-rectly to the preamplifier of each crystal, both peri-odic and random pulses from the 137Cs decay werecollected and processed together by a GRIF-16 fora given channel.

The GRIF-PPG module was used in conjunctionwith analogue electronics to control the measure-ment cycle, comprised of 10 seconds of measure-ment with the Pulser ‘on’ (Rc) and 10 seconds withthe Pulser ‘off’ (Rs). In this way no cables were un-plugged or connected when changing between (Rc)and (Rs). The first and last two precision deadtimescaler readings obtained during transitions betweenthe two states were omitted from the analysis. A di-agram of the test setup is shown in Figure 22. TheAND signal of the GRIF-PPG and Pulser gener-ated by an ORTEC CO4020 logic unit was used asinput to a ORTEC GG8020 Gate Generator. TheGate Generator was used to shape the width of theNIM pulser signal (≈ 3 µs) to ensure no modifica-tion of the signal processing algorithm in the GRIF-16 was necessary (an unmodified square-wave pulsefrom the Agilent pulser is too large and distorts theHPGe preamplifier output signal). A total of fourmeasurements were conducted, each using a differ-ent Pulser frequency, where Rp was varied from 2-20 kHz. Rs remained ≈3 kHz per HPGe channel.Each measurement lasted ≈90 cycles.

22

Energy (keV)

0 500 1000 1500 2000 2500 3000

No

rma

lise

d c

ou

nts

1

10

210

310

410

510

(a)

1.1 kHz

62.4 kHz

Energy (keV)

0 500 1000 1500 2000 2500 3000

No

rma

lise

d c

ou

nts

1

10

210

310

410

510

(b)

1.1 kHz

62.4 kHz

Figure 21: GRIFFIN energy spectra for (a) only single interactions, and (b) all interactions, collected using a 60Co source fora single HPGe channel at counting rates of 1 and 62 kHz. The spectra are normalized according to the number of counts inthe 1173 keV photopeak, corrected for the probability of detecting the full-energy. The feature at ∼600 keV in the high-ratespectrum is the result of Compton scattering from a piece of Pb shielding not present in the low-rate data. A number ofpeaks from room background can be seen in the low-rate spectrum including the radioactivity of 138La present in the LaBr3detectors.

23

ORTECCO4020

GG8020Gate Gen

erator

GRIF-PPGAgilent Pulse

HPGe preamptest inputAND

Figure 22: Schematic of the experimental setup used to mea-sure the fixed deadtime of the precision deadtime scalers.

Table 5: Summary of deadtime measurements performed fora single GRIFFIN HPGe channel. τdi is the non-extendingdeadtime imposed on each fixed-deadtime scaler channel andτdm is the deadtime measured according to Eq. 4. Rs,c arethe mean counting rates of the source and of the source plusPulser respectively, averaged over all measurement cycles.Rp is the Pulser frequency.

Rs Rp Rc τdi τdmkHz kHz kHz µs µs

2.425(47) 20 22.261314 0 1.71.3

1.7

2.421(47) 20 22.231314 1 2.01.0

2.0

2.370(46) 20 21.441114 10 9.91.1

1.4

1.951(35) 2 3.2475755 100 100.09.7

9.8

Results obtained for a single GRIFFIN HPGechannel are shown in Table 5. The results fromall nine channels tested are plotted in Figure23. For imposed deadtimes of 0,1 and 10 µs,the data correspond to tests performed using a20,000.000(20) kHz Pulser rate. For an imposeddeadtime of 100 µs, a 2,000.000(2) kHz Pulser rate(2 ms pulse period) ensured that the arrival timebetween pulses was greater than the imposed dead-time.

A combination of statistical analyses taking intoaccount both the non-random nature of the peri-odic pulses and the correlation between the uncer-tainties in Rs and Rc were used to determine thefinal uncertainty in τdm [19]. τdm and τdi agree for allchannels within uncertainty limits, typically within±10 % for τdi =10,100 µs, with larger relative uncer-tainties observed for smaller imposed deadtimes.

8. Precision Measurements

A thorough understanding of detector and elec-tronics pulse pile-up effects are especially importantwhen making precision measurements [20]. In addi-tion it is desirable for the deadtime of each detectorchannel to be determined with good accuracy. The

HPGe Channel

1 2 3 4 5 6 7 8 9

s)

µD

ea

dtim

e (

0

2

4

6

8

10

12

14

16

(a)sµ=0

iτ

sµ=1 i

τ

sµ=10 i

τ

HPGe Channel

1 2 3 4 5 6 7 8 9

s)

µD

ea

dtim

e (

75

80

85

90

95

100

105

110

115

120

125

(b) sµ=100 i

τ

Figure 23: Deadtime determined using Equation 4 plottedagainst GRIFFIN HPGe channel number for (a) imposeddeadtimes τi of 0, 1 and 10 µs and (b) 100 µs. Data obtainedfor τi ≤ 10 µs used a Pulser frequency of 20 kHz. Due to alimiting factor of the paired-source method where the arrivaltime of the periodic pulses must be greater than the imposeddeadtime, measurements with τi = 100 µs were performedusing a 2 kHz Pulser frequency.

24

GRIFFIN system provides the information in thedata required to assess these factors.

The precision deadtime scalers discussed in sec-tions 4.7 and 7.6 are not suitable for precision half-life measurements using HPGe detectors becauseof the relatively low peak-to-background ratio ingamma-ray spectra. The use of PMT signals withsuch scalers can also be unreliable. However thisfirmware could be employed with a detector such asthe 4π continuous gas-flow proportional β counterdescribed in Ref. [21] to make precision half-livemeasurements. This application will be looked atin the future.

The performance of the system for making pre-cision half-life measurements remains to be demon-strated but each of the required features are alreadyimplemented in the firmware and described in theearlier sections.

9. Future Development Plans

The system that has been implemented to dateuses 5 Gb/s links between digitizer and collectormodules, as well as from the GRIF-C Master mod-ule to the backend computer running MIDAS. A5 Gb/s link is more than adequate for the ∼34MB/sof data produced from 16 channels of HPGe count-ing at 50 kHz each, or for associated ancillary de-tectors. This link capacity is also sufficient to con-nect the GRIF-C Slave modules to the GRIF-CMaster module as long as a sufficient number areused. The master filter algorithm can process 1event per clock which is equivalent to 100 millionevents per second or ∼35 Gb/s. The present sin-gle 1 Gb/s link from the GRIF-C Master to theMIDAS system is a current limitation, throttlingthe overall DAQ through-put to <125MB/s. Thisimplementation has been used to demonstrate theperformance for a subset of the GRIFFIN array upto 50 kHz but limits global counting rate for thefull detector system. At the backend, the MIDASsystem has been demonstrated to operate at morethan 700 MB/s using 10 Gb/s network connectionsand a disk server.

It is planned to implement a 10 Gb/s link con-nection from the GRIF-C Master module to thebackend computer in order to relieve the mainthrough-put limit of the present system. The Se-rial RapidIO architecture [22] for high-performancepacket-switched, interconnection between all de-vices in the system will also be implemented, morefor standardization and firmware portability rather

than performance gain. The hardware was designedwith these capabilities in mind and the necessaryfirmware development will be completed in the nearfuture.

A fast-sampling FMC card is under developmentwhich will use the GRIF-16 module as a carrierboard. This card is based around the dual-channel,12-bit AD9234 ADC chip which will enable eitherfour channels of 500 MHz sampling, or two channelsof 1 GHz sampling. This card is at the prototypestage and will be used to process the signals directlyfrom the PMT output of scintillators.

A 32-channel, 65 MHz sampling FMC card is un-der development which will use the GRIF-16 mod-ule as a carrier. This is a cost-effective solution us-ing two AD9249 ADC chips for integrating a highly-segmented auxiliary detector system, such as a sil-icon barrel array similar to the SHARC detector[23].

10. Summary

A new digital data acquisition system has beencommissioned at TRIUMF-ISAC to collect datawith the GRIFFIN HPGe facility. The new systemis comprised of custom designed and built electron-ics modules. The aspects of the system suitablefor performing high-precision measurements rele-vant to the study of Fermi superallowed beta de-cays are discussed. The capabilities of the system tocollect data of good spectroscopic quality at count-ing rates up to 50 kHz per HPGe crystal has beendemonstrated.

11. Acknowledgments

N. Bernier, J. Measures and J. Pore are thankedfor their assistance in collecting data used to con-struct versions of some figures in this manuscript.A.B.G. is grateful for support from the Depart-ment of Nuclear Physics, Australian National Uni-versity during the preparation of this manuscript.C.E.S. acknowledges support from the Canada Re-search Chairs program. This work was supportedby the Natural Sciences and Engineering ResearchCouncil of Canada. The GRIFFIN infrastructurehas been funded jointly by the Canada Founda-tion for Innovation, TRIUMF and the Universityof Guelph. TRIUMF receives funding via a contri-bution agreement through the National ResearchCouncil Canada.

25

Appendix A. The probability of random-coincidence-summing andpile-up

If one assume a Poisson distributed process ofrate R, then the probability of there being no hitsin the following time period ∆t is

P (0) = e−R∆t. (A.1)

The probability that there is a hit in the time pe-riod dt is:

R(1) = Rdt. (A.2)

The variable t must be integrated over a period oftime to obtain a physical probability. These twoequations can be used to calculate the probabilityof different event types in the GRIFFIN DAQ sys-tem. We define an event as a grouping of occur-rences that are within a time period TE

PP of eachother. The first gamma-ray interaction, here la-beled as hit 0 at t0, opens up two windows: a fixeddead time of duration TH

DT and a pulse processingwindow of duration TE

PP . The pulse processing win-dow is equal to the TE

diff plus the risetime of thepulse. This is not a fixed time but the risetime isonly a small addition to the TE

diff . Any hits thatoccur before the end of the dead time window aresummed and not identified by the system as sepa-rate gamma-rays. Any interactions that occur afterthe end of the dead time window but before the endof the pulse processing window opens a new pair ofwindows and extends the possible time for otherinteractions to be grouped into this event. In ad-dition, in order to be the first hit, there must beno other hits in a time window TE

PP immediatelypreceding the initial hit.

In order for a hit to be a “single interaction”event, no hits should occur within the time periodTEPP on either side of t0. Therefore, using Equa-

tion A.1, the probability that hit 0 is in a singleinteraction event is:

P = e−2RTEPP (A.3)

When there is a second hit within the pulse pro-cessing window then it can either be summed orpiled-up. The probability of the two hits summingis equal to,

P = e−2RTEPPR

∫ TEDT

t1=0

dt1 (A.4)

= e−2RTEPPRTE

DT (A.5)

and the probability of the two hits being piled-upis,

P = e−2RTEPPR

∫ THPP

t1=THDT

e−Rt1dt1 (A.6)

= e−2RTEPPR

[− 1

Re−Rt1

]THPP

t1=THDT

(A.7)

= e−2RTEPP (e−RTH

DT − e−RTEPP ) (A.8)

.The general expansion of this to higher numbers

of hits must take into account the probability ofsumming occurring between any pair of hits in thefull pile-up event and is determined as

P = e−RTHDT

N∏i=1

(dtN ) e−Rte (A.9)

where N is the number of hits and te is either THDT

or TEPP depending on if it is a summing or pile-

up scenario. Table A.6 lists the equations for eachscenario involving up to four hits.

The probability for the various scenarios in whichthe true energy of the hit is detected, i.e. with nosumming, is shown in Table A.7.

References

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Methods in Physics Research 345 (1994) 770.

26

Table A.6: Probability calculations for the probability that a single gamma-ray interaction is the gamma-ray that begins aparticular type of event. Here, N takes the value of either the incident hits, observed hits or observed true-energy hits tocalculate the probability that a particular gamma-ray is in each of these scenarios.

Scenario Equation of Probability Incident Observed True-energy

hits hits hits

Single hit Ne−2RTEPP 1 1 1

2 hits summed Ne−2RTEPPRTH

DT 2 1 0

2 hits piled-up with no summing Ne−2RTEPP (e−RTH

DT − e−RTEPP ) 2 2 2

3 hits all summed together Ne−2RTEPP

(RTHDT )2

23 1 0

3 hits piled-up with hits 0 and 1 summed Ne−2RTEPPRTH

DT (e−RTHDT − e−RTE

PP ) 3 2 1

3 hits piled-up with hits 1 and 2 summed Ne−2RTEPPRTH

DT (e−RTHDT − e−RTE

PP ) 3 2 1

3 hits piled-up with no summing Ne−2RTEPP (e−RTH

DT − e−RTEPP )2 3 3 3

4 hits all summed together Ne−2RTEPP

(RTHDT )3

64 1 0

4 hits piled-up with hits 0 and 1, and

hits 2 and 3 summed separately Ne−2RTEPP (RTH

DT )2(e−RTHDT − e−RTE

PP ) 4 2 0

4 hits piled-up with hits 0, 1 and 2 summed Ne−2RTEPP

(RTHDT )2

2(e−RTH

DT − e−RTEPP ) 4 2 1

4 hits piled-up with hits 1, 2 and 3 summed Ne−2RTEPP

(RTHDT )2

2(e−RTH

DT − e−RTEPP ) 4 2 1

4 hits piled-up with hits 0 and 1 summed Ne−2RTEPPRTH

DT (e−RTHDT − e−RTE

PP )2 4 3 2

4 hits piled-up with hits 1 and 2 summed Ne−2RTEPPRTH

DT (e−RTHDT − e−RTE

PP )2 4 3 2

4 hits piled-up with hits 2 and 3 summed Ne−2RTEPPRTH

DT (e−RTHDT − e−RTE

PP )2 4 3 2

4 hits piled-up with no summing Ne−2RTEPP (e−RTH

DT − e−RTEPP )3 4 4 4

[14] J. Stein, et al., Nuclear Instruments and Methods inPhysics Research B 113 (1996) 141.

[15] B. A. VanDevender, M. P. Dion, J. E. Fast, D. C. Ro-driguez, M. S. Taubman, C. D. Wilen, L. S. Wood,M. E. Wright, IEEE TRANSACTIONS ON NUCLEARSCIENCE 61 (2014) 2619.

[16] E. R. Tardiff, et al., Hyperfine Interact. 225 (1) (2014)197.

[17] V. Bildstein, P. E. Garrett, S. F. Ashley, G. C. Ball,L. Bianco, J. B. D. Bandyopadhyay, B. P. Crider, G. De-mand, G. Deng, I. Dillmann, A. Finlay, A. B. Gar-nsworthy, G. Hackman, B. Hadinia, R. Kruecken, K. G.Leach, J.-P. Martin, M. T. McEllistrem, C. J. Pear-son, E. E. Peters, F. M. Prados-Estevez, A. Radich,F. Sarazin, C. Sumithrarachchi, C. E. Svensson, J. R.Vanhoy, J. Wong, S. W. Yates, EPJ Web of Conferences93 (2015) 07005.

[18] A. P. Baerg, Metrologia 1 (1965) 131.[19] Statistical Problems in Particle Physics, Astrophysics

and Cosmology, Imperial College Press, 2006, Ch.Asymmetric statistical errors.

[20] G. F. Grinyer, C. E. Svensson, C. Andreoiu, A. N. An-dreyev, R. A. E. Austin, G. C. Ball, D. Bandyopadhyay,R. S. Chakrawarthy, P. Finlay, P. E. Garrett, G. Hack-man, B. Hyland, W. D. Kulp, K. G. Leach, J. R. Leslie,A. C. Morton, C. J. Pearson, A. A. Phillips, F. Sarazin,M. A. Schumaker, M. B. Smith, J. J. Valiente-Dobon,J. C. Waddington, S. J. Williams, J. Wong, J. L. Wood,E. F. Zganjar, Nuclear Instruments and Methods inPhysics Research A 579 (2007) 1005.

[21] G. C. Ball, Hyperfine Interact. 225 (1) (2014) 133.[22] RapidioTMinterconnect specification.

URL http://www.rapidio.org/wp-content/uploads/

2014/10/RapidIO-3.1-Specification.pdf

[23] C. A. Diget, S. P. Fox, A. Smith, S. Williams, M. Porter-Peden, L. Achouri, P. Adsley, H. Al-Falou, R. A. E.Austin, G. C. Ball, J. C. Blackmon, S. Brown, W. N.Catford, A. A. Chen, J. Chen, R. M. Churchman,J. Dech, D. D. Valentino, M. Djongolov, B. R. Fulton,A. Garnsworthy, G. Hackman, U. Hager, R. Kshetri,L. Kurchaninov, A. M. Laird, J. P. Martin, M. Matos,J. N. Orce, N. A. Orr, C. J. Pearson, C. Ruiz,

27

Table A.7: Probabilities of true-energy hit detections at various incident gamma-ray rates. The last three columns capture allpossibilities and therefore their sum is equal to 1.

Incident THDT TE

dif Number of pile-ups Total full

rate (kHz) µs µs 1 2 3 >=4 Summing photopeaks1 1.2 8 0.984 0.013 0.000 0.000 0.002 0.9985 1.2 8 0.923 0.061 0.003 0.000 0.012 0.98810 1.2 8 0.853 0.111 0.011 0.002 0.023 0.97520 1.2 8 0.731 0.180 0.034 0.012 0.044 0.94430 1.2 8 0.627 0.220 0.059 0.033 0.062 0.90640 1.2 8 0.539 0.239 0.082 0.065 0.075 0.86050 1.2 8 0.464 0.244 0.099 0.107 0.086 0.80750 1.2 4 0.681 0.165 0.030 0.021 0.104 0.87650 1.2 6 0.562 0.221 0.066 0.056 0.095 0.84950 1.2 8 0.464 0.244 0.099 0.107 0.086 0.80750 1.2 10 0.383 0.247 0.124 0.171 0.076 0.75350 1.0 8 0.462 0.252 0.106 0.107 0.072 0.82150 1.2 8 0.464 0.244 0.099 0.107 0.086 0.80750 1.4 8 0.466 0.236 0.093 0.107 0.099 0.79450 1.6 8 0.468 0.227 0.086 0.107 0.113 0.78150 1.8 8 0.470 0.219 0.080 0.106 0.126 0.76850 2.0 8 0.471 0.211 0.074 0.106 0.139 0.755

F. Sarazin, S. Sjue, D. Smalley, C. E. Svensson, M. Tag-gart, E. Tardiff, G. L. Wilson, Journal of Instrumenta-tion 6 (2011) P02005.

28