The International Conference on E-Product, E-Service and E-Entertainment (ICEEE2010) Nov.4-6, 2010 in Henan, China http://www.ic3e.org Volume6 IEEE Catalog Number:CFP1096J-ART ISBN: 978-1-4244-7161-4

3411 978-1-4244-7161-4/10/$26.00 ©2010 IEEE

Simulation Study on 104 MHz Radio Frequency Quadrupole Accelerator

Y. C. Nie, Y. R. Lu, S. L. Gao, K. Zhu, X. Q. Yan, Z. Y. Guo, J. X. Fang, J. E. Chen State Key Laboratory of Nuclear Physics and Technology, School of Physics

Peking University Beijing, China

ycnie@pku.edu.cn

Abstract—An electrical model of the 104 MHz radio frequency quadrupole (RFQ) accelerator at Peking University is introduced for RF design, based on which every crucial geometrical parameter is swept and selected carefully to improve the RF properties of the RFQ such as the intrinsic quality factor and shunt impedance for reducing its power consumption. Moreover, flatness tuning of the inter-electrodes voltage is investigated in principle. Also, a magnetic coupling loop is designed for power feeding of the RFQ cavity from transmitter. Relevant numerical simulations are performed using 3D electromagnetic field program CST Microwave Studio (MWS).

Keywords-radio frequency quadrupole; equivalent circuit;MWS simulation; shunt impedance; flatness tuning; power coupling

I. INTRODUCTION

Radio frequency quadrupole (RFQ) accelerator has been widely used in beam injector, neutron source, etc [1, 2]. The two main aspects when designing a RFQ are beam dynamics and RF structure [3-5]. For the 104 MHz RFQ at Peking University aiming at 14C+ acceleration from 40 keV to 500 keV, the novel low-energy-spread beam dynamics design has been successfully realized using the internal discrete bunching strategy with RFQDYN program derived from PARMTEQ, instead of the external bunching method in [6]. On the other hand, considering the relatively high operating frequency, the ladder type IH-RFQ structure is adopted, which possesses the highest resonant frequency compared with traditional IH and 4-Rod RFQ under the same transverse dimension, by virtue of its H210 electromagnetic mode and the novel stem arrangement [7].

Figure 1. The 104 MHz ladder IH-RFQ with coupling loop.

In this paper, we will focus on the RF aspect of the RFQ design, including optimization of the structure parameters in order to minimize the power consumption, tuning measure of the longitudinal flatness of inter-electrodes voltage and RF power coupling. For integral and distribution parameters analysis, it is important to develop a suitable electrical model, and then carry out numerical simulations for the cavity using some powerful tools e.g. CST Microwave Studio (MWS) that has been widely used in 3D electromagnetic field simulation [8]. These issues will be presented in detail combining with the 104 MHz ladder IH-RFQ shown in Fig.1.

II. STRUCTURE MODELING AND OPTIMIZATION

A. Cavity Modeling and Analysis

There are many authors reported their studies on RFQ cavity modeling [9, 10]. The conventional electrical model can be shown as Fig.2, consisting of the equivalent resistance, inductance, capacitance and parallel shunt impedance, denoted by R, L, C and Rp, respectively. According to the definitions of intrinsic quality factor Q0=W/P and shunt impedance Rp=V2/P, with the resonant frequency =2f=1/(LC)1/2, average energy stored in one period W=1/2I2L=1/2CV2 where I is peak current and V is peak voltage, and power dissipation P=1/2I2R, we have

Q0=1/R(L/C)1/2=Rp/2(C/L)1/2. (1)

For RFQ cavity having N basic resonant cells, the relation between the total R, L, C, I and corresponding values of single cell Rcell, Lcell, Ccell, Icell will be

R=Rcell/N, L=Lcell/N, C=NCcell, I=NIcell (2)

when ignoring the end effect. Combining (1) with (2) we find

Q0= Q0,cell and Rp= Rp,cell/N, (3)

where cell denote the values of single cell. For ladder IH-RFQ, Fig.3 shows the simplified circuit of one cell with

Rcell=Rstem/2, Lcell=Lstem/2, Ccell=2Cstem+Crod. (4)

In (4) it is assumed that the resistance and inductance are mainly attributed to the stems, while the capacitance arises from the two pairs of opposite electrodes and adjacent stems with Crod several times greater than Cstem generally.

Supported by the National Natural Science Foundation of China under Grant No 10775009.

stem

electrode

tuning plate

coupling loop

coaxial waveguide

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Figure 2. Equivalent circuit of RFQ cavity.

Figure 3. Equivalent circuit of single cell for ladder IH-RFQ.

B. Cavity Simulation and Parameter Optimization

Mode analysis of the RFQ was performed using the eigenmode solver of MWS. Fig. 4 shows the electric field, magnetic field and surface current distribution. These results agree with the H210 mode and the expectation from Fig.3.

(a) electric field among electrodes (up) and stems (bottom)

(b) magnetic field distribution

(c) surface current flow

Figure 4. MWS-simulation results of the electromagnetic field and surface current flow of the ladder IH-RFQ.

The RFQ structure is optimized by parameter sweeping [11] to achieve the maximum Q0, Rp, and minimum P at 104 MHz. Some conclusive results are as follows.

1) Stem number N: The beam dynamics design established the inter-electrodes aperture and the electrode length, therefore the first parameter to be studied is the stem number N used. Bigger N means shorter distance between adjacent stems d, leading to decreasing Lcell and Ccell, but slightly increasing Rcell in view of more serious proximity effect. Taking (2) into account, R, L will decrease while C increase because of the increment in Cstem, finally resulting in bigger f as illustrated by MWS simulations. The cavity diameter D has to be scaled to keep f 104 MHz. Fig.5 shows the relevant simulation results, according to which 10 stems was employed.

(a) structure parameters

I/2

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(b) RF properties

Figure 5. Variations of RFQ parameters with stem number.

2) Cavity diameter D: As a variable D is always used to make f unaltered when sweeping the other parameters. When f needs to be lowered, D should be extended to make Lstem, Cstem as well as Rstem bigger.

3) Stem spacing d: Over the 95 mm to 115 mm d range in 5 mm increments with N=10, f decreases while Rp and Q0 increase due to smaller Cstem, Rstem and bigger Lstem with increasing d. After adjusting D, it was found that Rp and Q0 are approximately proportional to d, taking into account the end effects and the mechanical feasibility d=110 mm was eventually chosen.

4) Stem width Wstem: The increase in Cstem, and decrease in Lstem as well as Rstem with Wstem over the simulation range result in increasing f and Q0 but decreasing Rp. By adjusting D, it could be seen that there is a peak value of Rp, this is why Wstem=130 mm was adopted to make power loss least.

The optimization results are listed in Table I.

TABLE I. OPTIMIZATION RESULTS OF THE RFQ

Resonant frequency (MHz) 103.6

Cavity length (mm) 1121

Cavity diameter (mm) 720

Stem number 10

Stem spacing (mm) 110

Stem width (mm) 130

Intrinsic quality factor 6150

Shunt impedance (kΩ) 114

Power consumption (kW) 32 (V=60kV)

Coupled frequency (MHz) 103.9

Coupling loop area (cm2) 50

Loop-Stem distance (mm) 4

S11 parameter (dB) -20

III. FLATNESS TUNING OF INTER-ELECTRODES FIELD

The inter-electrodes voltage is usually supposed to be constant longitudinally when carrying out the beam dynamics design. So it has long been an important topic that how to tune the voltage unflatness of RFQ owing to the end effect and modulated electrodes to ensure a good beam quality. For ladder IH-RFQ, adjustable tuning plates as in Fig.1 can be inserted into neighboring stems symmetrically up and down, which is developed from the case of 4-Rod RFQ [12]. The tuning plates serve as short pieces of stems, changing their inductances thus the frequency and field strength. To verify their tuning capability, corresponding simulations were performed for tuning plates’ height 0, 50 and 100 mm, of which the results are plotted in Fig.6. Here electric field is equal to voltage between relevant electrodes, since the electrodes are unmodulated with uniform aperture radius. It can be seen that the field unflatness achieves its optimum value 2% when the tuning height is 100 mm. Tuning plates cause increment in the eigenfrequency of RFQ, so f is generally set to be several percents lower than desired value to leave enough tuning space.

Figure 6. Variations of field flatness with tuning plates height.

IV. POWER COUPLING

Magnetic coupling loop with coaxial waveguide is widely used in power feeding of the RFQ [13-15]. The equivalent circuit of the coupling system is shown as Fig. 7 with the mutual inductance M and the loop’s self inductance Lc. To meet the critical coupling condition between the loop and RFQ, the imaginary part of the input impedance for coupled RFQ Zin should be 0, meanwhile the real part should equal the impedance of the waveguide Z0=50 Ω, therefore

0 p

0 0

/ 2R RM

Q and

2 220 0

c 0 20 0 0

1R

L QQ

, (5)

where ω and ω0 are the eigenfrequency with and without the coupling loop, respectively. For given cavity RF properties, the critical coupling can be realized by adjusting M. On the other hand, Lc increases the eigenfrequency slightly, meanwhile if

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the electric field is strong near the coupling loop f will be lowered appreciably due to parasitic capacitance.

The loop area S and position for ideal M can be identified primarily by rough calculation. Assuming the mean magnetic field in the loop plane is H, then combining (1), (5) with M=0HS/I where 0 is the magnetic permeability of vacuum, S can be estimated by

0 p 0

0 0 0 0 0 0

/ 2 2Z R Z PMI IS

H Q H H . (6)

This is consistent with the method that derives S by equating the voltage excited in the loop by a generator Vg with the voltage induced in it by the magnetic field of the cavity, i.e.

Vg=00HS, (7)

where Vg=(2Z0P)1/2.

From one group of MWS simulation, the magnetic field component perpendicular to the loop plane Hz is shown in Fig.8 when the cavity power consumption is around 100 kW. It is obvious that the closer the loop is to the stem, the smaller the loop area required can be. Supposing the average of Hz in the loop plane is about 1000 A/m, the loop area needed will be about 40 cm2 according to (6). On this basis, an optimum design of the coupling loop has been achieved by means of MWS transient solver, shown in Fig.1, corresponding to which the S11 parameter of the coaxial waveguide port reaches -20 dB. These results are listed in Table I.

M

Figure 7. Equivalent circuit of RFQ with coupling loop.

Figure 8. Distribution of longitudinal magnetic field component for the RFQ.

V. SUMMARY

An equivalent circuit model for ladder IH-RFQ was presented, depend on which the cavity was optimized to reduce power consumption for given resonant frequency and desired inter-electrodes voltage, with the help of MWS simulations. The tuning measure of voltage flatness was verified in principle for the RFQ. As for the power feeding, a coupling loop was designed based on theoretical analysis and transient simulations. Up to now, all the RF design works have been finished. Experimental study will be carried out after the RFQ cavity is manufactured within this year according to schedule.

ACKNOWLEDGMENT

The authors would like to thank Prof. Dr. U. Ratzinger of IAP, J. W. Goethe University Frankfurt am Main for his assistance and support in the cavity simulations. Y. C. Nie also thanks the China Scholarship Council (CSC) for financial support when he was in Frankfurt.

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