New plasma sources for long laser wakefield plasma accelerators

Carlos RussoR. Bendoyro, J. Jiang, L. CardosoG. Figueira, N. Lopes.

P2.213Dublin, June 22, 201037th European Physical Society Conference on Plasma Physics

http://golp.ist.utl.pt/Grupo de Lasers e Plasmas

Motivation

Conventional accelerators are huge

๏ SLAC : 50 GeV in 3.2 km

๏ ILC (2012+): 250 GeV in 12 km

๏ (LEP : 209 GeV in 27 km)

Laser-plasma accelerators

๏ 100 MeV mono-energetic bunches

๏ bunches of 1 GeV in 3.3 cm

๏ (42 GeV ➝ 84 GeV e- in 85 cm)

Mangles et al. Nature 431, 535 (2004)Geddes et al. Nature 431, 538 (2004)

Faure et al. Nature 431, 541 (2004)

Leemans et al. Nature Phys. 2, 535 (2006)

limited toE < 55 MV/m

E ~ 100 GV/m

Blumenfeld et al. Nature 445, 741 (2007)

electrons

Laser-plasma accelerators

1 mw0 = 54μm

15 GeV

0.8 nC

Energy gain limited by depletion, dephasing and interaction lengths

Quality of beams best at low intensitiesSelf-guiding might not be possible!

Extend length by guiding light in preformed plasma channels

2.5 PW50 J, 20 fs

Durfee, Milchberg, PRL 71, 2409 (1993)Butler, et al., PRL 89, 185003 (2002)

electrons laser plasma channel

Structured gas cellBENDOYRO et al.: PLASMA CHANNELS FOR ELECTRON ACCELERATORS USING DISCHARGES IN GAS CELLS 1729

Fig. 1. (Color) Side-view schematic of the structured gas cell.

II. STRUCTURED GAS CELL DEVICE

The devices under consideration are intended to be usedas plasma electron accelerators and should produce a straightplasma column coaxial with the driving laser pulse with thefollowing requirements: 1) radially parabolic density profilewith minimum on axis in order to guide the driving laserwith constant intensity over the guiding length; 2) a guidingplasma region close to full ionization so the driver cannotproduce further ionization changing the refraction index profile;3) a guiding length close to the dephasing length (the lengththat a relativistic electron takes to overcome the accelerationplasma structure, dependent on the plasma density and thedriver wavelength); and 4) the plasma waveguide should allowan efficient coupling of the laser driver.

A side-view schematic of the structured gas cell is shown inFig. 1. In order to extend the acceleration length to the max-imum in a single stage and keep the possibility of transverseoptical access to the plasma (for optical diagnostics and inter-action with transverse intense laser beams), we decide to keep afree expansion plasma as in previous laser-triggered dischargeplasma channels [14]. However, to avoid laser triggering of thedischarge, we use higher voltage pulses (gap initial electricfield of about 50 kV/cm) with a short (sub 5 ns) rise timeand we divided the gas cell space between electrodes with asequence of thin dielectric plates with micromachined smalldiameter apertures on the guiding axis (defined by the aperturesin the apexes of the copper-made conic electrodes). The purposeof the short rise-time high-voltage pulse is to produce theinitial plasma in a reproducible way, and the purpose of thedielectric aperture sequence is to set the initial plasma diameterand position in space because the discharge is forced throughthe dielectric apertures. In order to make the effects of thepresence of the dielectric plates negligible for laser guiding,they are separated by a distance at least ten times larger thanthe thickness of the plates, and the aperture diameter is largerthan the plate thickness. The electrodes have a conical shape sothe discharge initiates reproducibly on the cone apex. A smallaperture is drilled on the apex so the laser beam can propagatethrough the electrodes. The thickness of the electrodes on theapex should be minimum in order to reduce any interfaceeffect of the guiding channel with vacuum that may reducethe coupling efficiency. The electrodes sit on a metallic mount

that interfaces with the high-voltage transmission line with theminimum inductance and capacitance.

In order to achieve total ionization, we use hydrogen as thebackground gas. The gas injection is controlled by a fast valve(Parker ref. 009–0631–900) synchronized with the laser and thedischarge. The gas injection is reproducible for electric pulsesof 40 V with durations greater than 2 ms (the valve has a 24-Vdc solenoid). This valve is connected upstream to a cylinderwith a volume of 1 L, used to keep the gas pressure constant. Itis connected downstream to the device by a 1/4-in plastic tubewith a length of 20 cm. In this connection, there is a pressuresensor close to the valve used to verify the reproducibility of thegas injection. The minimum absolute pressure inside the gascylinder is 1.2 bar (±10%) limited by the pressure regulator.The gas pressure can be estimated by measuring the plasmaelectron density (assuming full ionization before significantexpansion). In this way, for current configuration, we estimatethe minimum pressure (using 1.2-bar backpressure and 2-mspulses to open the valve) as 20 mbar. The maximum pressure islimited to less than 1 bar by the window sealing.

The holes on the electrode apexes are leaks from the gas cellto the main vacuum system, but the device design allows for ahigh conductance gas pulsed injection (when compared withthese leaks) resulting in the fast creation of a target volumeof gas inside the gas cell. This fast injection contributes for areduced leak of nonionized gas to the path of the main beam,reducing the effects of ionization-induced defocusing.

The prototype under analysis has a distance between elec-trodes of 16.6 mm and uses eight thin dielectric plates made of250-µm-thick alumina with 300-µm-diameter apertures on theaxis that are spaced by 2.25 mm. The copper electrodes havea hollow double conic shape with 300-µm-diameter apertureson the tip and are placed at 0.3 mm from the closest dielectricaperture. The resin body is connected to a rigid dielectric framethat is connected by stainless steel bellows from both sidesto vacuum chambers. Although we are using the device as anexternal gas cell, it can be adapted to be used inside a biggertarget chamber.

III. HIGH-VOLTAGE PULSE GENERATION AND DELIVERY

The present laser guiding scheme requires the use of a high-voltage discharge to produce the plasma channel. Because theplasma is not contained, it requires an initial electric field thatwe, conservatively, estimate as 50 kV/cm in order to producea straight plasma line through 2.25-mm-spaced apertures. Thisestimation was based on preliminary experiments. In order tohave a reproducible behavior of the discharge, and thereforethe plasma time evolution, the plasma needs to be created underthe same electric field. This can be achieved if the high-voltagepulse rise time is reduced to less than the time the dischargetakes to be initiated. The maximum required pulse duration wasestimated to be about 100 ns because this is the typical timefor a plasma created by a discharge to evolve into a guidingchannel. A high pulse current (!1 kA) is required to produce afast (!100 ns) channel with low density on the axis.

In order to satisfy these requirements, a design basedon a capacitive discharge with a thyratron switch using a

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Dielectric platesthickness: 250 micronspacing: 2.25 mmdrillings: ∅300 micron

Copper electrodesholes: ∅300 micron

Scalable to longer lengths

Experimental Setup

20 mm gas cell (H2)

High-power, HV pulser

Low-power, HV DC

Current and voltage diagnostics

Detection of recombination

Electron density

Vacuum

HV DC

power

supply

Vacuum

Spark-gap High-power

transmission line

InductorInductor

Resistor

Resistor

Capacitor

Window

Window

Gas cell

High-voltage

pulse generator

Coupled

Inductors

Current

Transformer

D-dot

Sensor

up to 100 kVup to 1 kArise time 20 nsduration 200 ns

20 kV1 mA

Mach-Zehnder interferometer

Experimental setup

High Voltage Pulser

๏ up to 100 kV pulserise time: < 20 nsduration: ~ 2 μs

๏ capacitive discharge(capacitor loaded up to 25 kV)

๏ triggered by a thyratron

๏ spark gap reduces jitter

๏ magnetic compressionincreases slope

Bendoyro et al., IEEE Trans. Plasma Sci, 36 1728 (2008)

Transmission Line TransformerThyratronUses magnetic compression

Interferometer

delay line

beam

probe

reference

Diagnostics

Current transformer

Voltage: D-dot signal

Plasma recombination (photodiode)

current

d-dot

∝ d| �D|dt

∝ dφ

dt

Experimental setup

Cell: 20 mm

Simmer discharge (DC)

๏ 20 kV power supplycharges capacitor

๏ slow rise time (ms)

๏ inductors protectfrom main HV pulse

๏ resistor limits current( R = 20 MΩ)

20 kV

Example shot

current

d-dot

laser pulse

PD signal

trigger tothyratron

Waveguide formation

ne (cm−3)

r (µm)

Average linear electron densityne · Splasma =

� 2π0

�∞0 ne(r)rdrdθ

Time-resolved electron density

Waveguide properties

3500 4000 4500 5000

−1500

−1000

−500

0

500

1000

15000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 1018

tran

sver

se d

irec

tion

(µm

)

transverse direction (µm) longitudinal direction (µm)

electron density (cm-3)

wm = 4

�r2ch

π · re ·∆ne

Matched spot size

transverse direction (µm)

elec

tron

den

sity

(cm

-3)

ne(r) = ne0 +∆ne

�r

rch

�2

wm = 87µm

wm ≈ 50 . . . 150µm

Interferogram analysis: procedure

Retrieve optical phase shift

๏ FFT, shift, invert FFT

Reconstruct radial profile

๏ Abel inversion

• obtain index of refraction, electron density

ne(r) =�1− η2(r)

� 2πmeε0λe2

ϕ(x, y) = FFT−1{�log�eikxFFT(I(x, y))

�}

2π

λη(r) = − 1

π

� ∞

r

∂ϕ(x, y)

∂y

dy�y2 − r2

k

ϕ(x, y)

stripe spatialfrequency

FFT

DC

Electron density profile

Matching conditions

wm = 4

�r2ch

π · re ·∆ne

Matched spot size

ne(r) = ne0 +∆ne

�r

rch

�2

Plasma channel

wm = 77.2µm

Demonstration of guiding

Plasma channel

๏ ne(0) = 3×1017 cm-3

๏ ne(r0) = 1×1018 cm-3

Probe beam

๏ in: F/30, ∅52 micron

๏ out: ∅46 micron

1732 IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 36, NO. 4, AUGUST 2008

Fig. 7. (Color) Line-out of the plasma density obtained from the interfero-gram of Fig. 6 (approximately in the middle of the visible cell). The density onaxis is 3.1 ! 1017 cm!3, the maximum plasma density on the channel wallsis 1.05 ! 1018 cm!3, and the channel radius is 405 µm.

for interferogram readability. It was obtained by using the samehigh-voltage pulse as in Fig. 5 but with a delay of 75 ns.We are not able to measure the pressure but, because forthese discharge parameters, the hydrogen ionization is close tocomplete, we can estimate it to be !20 mbar using the inter-ferometry results. The assumption of close to full ionizationis based on previous work where full ionized plasmas werecreated by similar discharges with the same hydrogen or heliumpressures and with lower electric fields and currents [14], [18].The plasma density is obtained using the same procedure as in[14]. First, the interferogram phase is obtained by manipulationof a clean part of the interferogram image in the frequencydomain [19]. Then, the refractive index, or the plasma density,can be retrieved by Abel inversion. There are two sensitiveaspects on this procedure. First, the phase is obtained usingfiltering and translation in the frequency domain. Filtering cutsout unwanted unphysical density oscillations but may also cutdetail (particularly important for plasmas with strong gradientslike the present ones). In our case, we try different filter sizesto make sure we are removing the oscillations due to the inter-ference, keeping the plasma density detail as much as possible(normally an error of less than 10% is achieved). The secondsensitive aspect is that Abel inversion works for symmetricobjects and requires an integration from the axis of the plasmato some distance where the plasma density is negligible. Here,we use the vertical phase “center of mass” as the plasma axisposition, and we average both sides of the plasma in order tosimplify the procedure. Nevertheless, the averaging does notintroduce significant changes because the plasma asymmetry isnormally negligible.

In Fig. 7, we present a line-out of the plasma density obtainedfrom the interferogram of Fig. 6. A clear close to parabolicshape with a minimum density on axis is obtained. The axialplasma density is 3.1 " 1017 cm#3, whereas the maximumdensity on the plasma channel wall is slightly higher than the1.05 " 1018 cm#3 shown on the graphic because it is affectedby the frequency space filtering. The diameter of the plasma

Fig. 8. (Color) Images of the transmitted laser beam at device exit (cathodeaperture) with (a) no plasma and (b) a plasma channel produced by a dischargewith a 65-ns delay. A circle on the aperture position was drawn on its position.The exit spot diameter on (b) is "46 µm.

channel (measured between density peaks) is 810 µm. Thematched guiding spot radius of this channel [20] is therefore!65 µm.

A plasma channel with this density and diameter can be usedwith a large laser system to produce energy gains on the order of10 GeV if the channel length is extended to !10 cm. However,an improvement on the interferometry diagnostic should makepossible the measure of plasmas of smaller diameter using thesame device.

The device can produce straight, uniform, and close tosymmetric plasmas that evolve to guiding plasma channels ina reproducible way for low gas cell pressures (20–40 mbar).When we increase the pressure above this region, the plasmasbecome less symmetric and reproducible.

VI. LASER GUIDING MEASUREMENTS

In Fig. 8, we present two images of the laser beam transmit-ted through the guiding device with no plasma (a) and with aplasma channel (b) produced with a delay of 65 ns after thedischarge current start. The images are taken in the cathodeelectrode aperture (the channel exit). The main probe laserbeam is focused in the capillary entrance with a focal spotdiameter of 52 µm.

The plasma channel used to obtain the image of the guidingbeam in Fig. 8(b) was produced with approximately the samegas cell pressure as the channel previously analyzed by inter-ferometry (close to 20 mbar). However, the delay of the laserbeam with respect to the discharge is 65 ns. This is 10 ns earlierin plasma expansion than in the interferometry shot where thedelay was 75 ns.

The spot size at the channel exit in Fig. 8(b) is !46 µm. Thisis a typical result in a guiding window of about 5 ns where weget very good reproducibility (!90%) laser guiding with spotsizes around 50 µm.

Outside the window, we can see no guiding for longer delaysand a progressively weaker guiding effect !20 ns before theguiding window. With the present setup, it is not possible tomeasure the guiding efficiency of the plasma channel. However,an estimate based on the integration of the image intensityfor different shots (to reduce the effect of shot to shot energyfluctuations) places this efficiency very close to one on theguiding window.

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HV: 96kV, 760AH2 at 20 mbar

Bendoyro et al., IEEE Trans. Plasma Sci, 36 1728 (2008)

P > 20 mbar: shot variation

Low p⋅d ( < 200 Torr⋅cm)

๏ Vbreakdown(pd) has a minimum

๏ Townsend mechanism

High p⋅d

๏ transition to streamer regime(faster dynamics)

see e.g. P. Raizer. Gas Discharge Physics. (1997)

BREAKDOWN AT LOW GAS PRESSURES

AIR CAR* (Fe. Zn. AJ. Brass), *irz (Ni). MCYCR(Brass)HOLSTand KJOOPMANS (Ag)

CAM (Fe.etC). EHHfNKRAN* (Ft)

PENNING and ADDINK (Fe)

235 10 2030 SO 100 2OOSOO SOO KJOO

p d (mm Hg x cm)

FIG. 2.2. Typical breakdown voltage curves for different gases

between parallel plate electrodes. pQ is the gas pressure in mm. Hgcorrected to C.

50 IOO ISO 2OO 2SO 300 350 4OO 450

pQd (mmHgxcm)

FIG. 2.3. Breakdown voltage curves in neon-argon mixtures

between large parallel plates at 2 cm. spacing. p is the gas pressure

in mm. Hg corrected to C.

except helium decrease, as far as is known, the breakdown voltage of

neon. In the case of helium the ionization potential is higher than that

of neon.

Paschen curve

192 EXPERIMENTAL STUDIES OF CH. IV

The principal characteristics of discharges between a negative point

and a positive plane is that, in addition to the negative leader starting

from a cathode, a positive leader stroke rises from the plane to meet the

Fio. 4.14. Drawing based on a rotating-camera photograph of a positive point-plane

discharge across a 50-cm. gap in air at 100 mm. Hg. A point of length 1 cm. projects

from the plane. The voltage curve gives the variation of voltage across the gap. Series

resistance ^ 100,000 Q.

descending negative leader. A typical photograph showing the growth

of a discharge across a 100-cm. gap between a negative high-voltage

point and an earthed plane, for R O6 MD, is given in Fig. 4.15, PL 5

[49]. The discharge starts from the cathode point as a series of sharply

defined stepped leader strokes, each of which extends the path traced

Spark discharge

Spark is transient

๏ one of multiple streamers “survives”

๏ rapid heating: shock wave

Solution: “Simmer” DC discharge

Define plasma line

๏ use weak pre-discharge (ms)

๏ low-impedance path

Rapid heating

๏ high-power spark (10s ns)

๏ expansion: plasma channel−10 −5 0 5 10 15 20 25

0

0.2

0.4

0.6

0.8

1

Time (ms)

Recom

bination(a.u.) Thyratron

switching off

Thyratron switching onhigh power discharge

Gas injection

Improvement by factor of 5

mean ± std

smaller voltage!

higher current!

p0 = 500 mbar

Reduced jitter

−10 −5 0 5 100

0.2

0.4

0.6

0.8

1

Delay (ns)

laser-disch jitter

−10 −5 0 5 100

0.2

0.4

0.6

0.8

1

Delay (ns)

Frequ

ency

(norm.)

laser jitter

−10 −5 0 5 100

0.2

0.4

0.6

0.8

1

Delay (ns)

discharge jitter

no DCwith DC σ = 1.5 ns σ = 1.9 ns

σ = 1.2 ns σ = 4.6 ns

Summary

Structured gas cells

๏ freely expanding plasma, laser triggering not necessary

๏ allows tailoring of gas density

๏ allows direct access to plasma

Studied reproducibility in a 2 cm device

๏ Characterisation of plasma channels

๏ Simmer discharge improves shot-to-shot variation

๏ higher p⋅d is now possible: longer channels

See alsoP2.203P2.224

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