Proceedings of IBIC2012, Tsukuba, JapanTUPB69NUMERICAL ANALYSIS ON THE GAIN-REDUCTION
CHARACTERISTICS OF MULTI-WIRE PROPORTIONAL CHAMBERS
Ken Katagiri, Takuji Furukawa, and Koji Noda,
Dept. of Accelerator and Medical Physics, National Institute of Radiological Sciences, Chiba, Japan
In order to investigate the gain-reduction characteristicsof the multi-wire proportional chamber (MWPC) fordifferent geometric parameters, we performed numericalsimulations using a numerical code. The numerical code
was developed using a two-dimensional drift-diffusion
model to evaluate the gas gain taking into account thereduction effect caused by the space charge effect of themoving positive ions. We investigated the gain-reduction
rate for several parameters of the anode-anode distancewhen beam intensity was increased. We found that thegain reduction could be improved by decreasing theanode-anode distance, owing to the sharing of the initialion pairs among the anode wires. From these results, wediscuss a desirable distance between the anode wires toimprove the gain reduction.

INTRODUCTION
Several tens of MWPCs have been installed in the beamtransport line at HIMAC (Heavy Ion Medical Acceleratorin Chiba) to diagnose the beam profiles [1]. Also in thescanning irradiation system, which was started to beoperated for the cancer treatment in 2011, the MWPCs
are used to evaluate the beam position and to construct 2D fluence maps [2]. In normal operation for treatments,
the MWPCs are operated in the current mode andirradiated by high-rate incident particles of ∼108 − 109
particles per second (pps). Under such a beam condition,
gain reduction of the output signal is observed. The gain
reduction is due to the distorted electric field, which
originates from the space charge of the accumulated ions.
If the gain reduction is large, the measured beam profiles
may differ from the actual profiles. Therefore,
modification of the MWPCs to suppress the gain
reduction is an important issue.
In the treatment operation at HIMAC, the irradiation
period of ∼1 s is much longer than that required by ionsto travel from the anodes to the cathodes. Therefore, thegain reduction process cannot be explained only by theremaining ions around the anodes, and it is expected to betransient during the beam irradiation. Information on therelations between the gas-gain variation and the iondensity distribution is necessary for modification of theMWPC parameters, such as anode radius and distance
between electrodes. For those reasons, we developed a 2D simulation code to evaluate the gas gain taking into
account the gain-reduction effect [3].
Using the numerical code, we performed analyses on thedynamics of ions/electrons in a helium-filled MWPC toimprove the gain reduction. In this paper, we report thesimulation results of the gas gain for several parametersof the anode-anode distance. Also we discuss the transient
dynamics of the ions, which leads to the variation of theoutput signal.

SIMULATION METHOD
The 2-dimentional drift-diffusion model was employed
to analyse the dynamics of the ions and electrons. In order
to simplify the analysis, electrons (e-) and positive ions(He+) were only taken into account. The two advectiondiffusion equations and the Poisson equation werecoupled and solved numerically. The pressure and thetemperature inside the MWPC were assumed to be 105 Pa
and 300 K, respectively. Figure 1(a) – (c) show schematic
diagrams of the MWPC in a discrete space. Three types of
MWPC with different anode-anode distance wereconsidered for comparison. The 6 6 mm region of theMWPC were discretized by rectangular grids. The anodeanode distance d was altered by changing the number of
the anode wires in 6-mm region: 1 wire for d = 6 mm (Fig.
1(a)), 2 wires for d = 3 mm (Fig. 1(b)), and 3 wires for d= 2 mm (Fig. 1(c)). The periodic boundary condition wasapplied to the boundaries at x = −3 mm and 3 mm. The
outlet boundary condition was applied to the surface ofthe two cathodes at y = −3 mm and 3 mm, and to thesurface of the anodes. Incident projectiles were injectedwith constant rate of I = 5 108 pps from t = 0. The beamprofile formed by all the projectiles was determined to bea Gaussian distribution of 2σ = 3.0 mm, as shown Fig.
1(d). The beam profile along the z-axis was assumed to behomogeneous in the depth direction of 3 mm. The numberof the ion-pairs was determined by W-value and energy
deposition of 350-MeV/u projectiles in 1-atm He gas [3].

RESULTS AND DISCUSSION
Conditions for Comparisons of the Gainreduction Characteristics
Figure 2 shows the calculation results of the gas gain
without the gain reduction. In order to calculate the noreduction regime, the space-charge effect was excluded
by considering the low rate beams. In order to compare
the gain-reduction characteristics, the applied voltages ofthree types of MWPC need to be determined to obtainsame gas gain in the no-reduction regime. For that reason,
the applied voltages were determined to obtain the gas
gain of M = 30: V = 847 V for d = 2 mm, V = 751 V for d= 3 mm, V = 674 V for d = 6 mm.

ISBN 978-3-95450-119-9
Transverse Profiles, Screens & Wires Monitors

1c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○Abstract

TUPB69

Proceedings of IBIC2012, Tsukuba, Japan30

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d = 6 mm (1 wire/6 mm)
d = 3 mm (2 wires/6 mm)
d = 2 mm (3 wires/6 mm) !µ"$& '()       10

1200$   % &!" !)" 300

400 500 600 700Applied Voltage V (V)

800

900

Figure 2: Gain curves without the space-charge effect.

c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○Gas Gain M#



674 V 751 V 847 V 

The results of reduction rate are 30% for d = 2 mm, 35%
for d = 3 mm, and 48% for d = 6 mm. From those results,
we confirmed that the gain reduction could be improvedby reducing the anode-anode distance.
We evaluated the total number of ions in MWPC, whichwere produced by electron-multiplication processes! " ! "Figure 3: Temporal evolution of gas gain.
Figure1: Schematic diagram of the MWPC of (a) d = 6 mm, (b)d = 3 mm, and (c) d = 6 mm. (d) The initial distribution of ionpairs.

Gain-reduction Characteristics
In order to compare the gain-reduction characteristics forthree types of MWPC, we calculated the variation of thegas gain from t = 0 to t = 25 µs. Figure 3 shows thetemporal evolutions of the gas gain for three types ofMWPC. Although each of three curves reached the gasgain of M = 30 at t = 0, they drastically decreased during
25 µs. In order to evaluate the gas gain after the transient
decay, each of curves was fitted by a function of y =const. using t = 20 – 25 µs region, as shown in the Fig. 3.

(avalanche), to consider the reason of the improvement on
the gain reduction. Figure 4 shows the temporal
evolutions of the total number of the ions in MWPC. The
ion dynamics in the 6-mm-distance MWPC did not reachthe quasi-stationary state [3] during 25 µs, as we can see
the transient variation in the curve. On the other hand, thegas-gain variation for the 6-mm-distance shown in Fig. 3
was in the end of the transient process and nearly constant.
Also, for example at t = 15 µs, we can see the least
number of ions in the 6-mm-distance MWPC, however its
gain-reduction rate was most intense for three types of theMWPC. This is due to fact that the gain variation wasstrongly affected by the ions around the anodes.

ISBN 978-3-95450-119-92Transverse Profiles, Screens & Wires Monitors

Proceedings of IBIC2012, Tsukuba, JapanTUPB69          by increasing the number of anode wires. Therefore, wecould decrease the ion density around each anode. Owing
to the low-ion density around the anode wires, the fielddistortion of the electric field was weakened. As a result,
we could improve the gain-reduction rate by increasing
the number of the anode wires.

CONCLUSION

Figure 4: Temporal evolutions of the number of ions.

Figure 5 shows the ion density distribution for (a) d = 6mm, (b) d = 3 mm, and (c) d = 2 mm. We see that the ionsdrifted from the anodes to the cathodes along theelectrical flux lines. By comparing the results from three
types of the MWPC, we confirmed that the ion density
around the anodes decreased as reducing the anode-anodedistance. When the fluence distribution of the incident
beams is same condition for three types of MWPC, theanode wires existing in the irradiation region share theinitial-ion pairs; The avalanche events around each anode,
which are caused by the initial-ion pairs, can be reduced

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Using a 2-D simulation code based on the drift-diffusion
model, we performed analyses on the dynamics ofions/electrons in a helium-filled MWPC to improve thegain reduction. From the simulation results, we found thatthe gain reduction caused by high-intensity incident
beams could be relaxed by the sharing of the initial-ion
pairs among the anode wires. In order to further optimize
the MWPCs used for beam profile monitor in the HIMAC
facility, we are going to investigate the dependence ofother parameters, such as the anode-wire radius and theanode-cathode distance, on gain-reduction rate.

REFERENCES[1] M. Torikoshi, et al., Nucl. Instrum. Meth. A, 435(1999) 326.
[2] T. Furukawa, et al., Med. Phys., 37 (2010) 5672.
[3] K. Katagiri, et al., Rev. Sci. Instrum., 82 (2011)053303-1.

ISBN 978-3-95450-119-9
3c 2012 by the respective authors — cc Creative Commons Attribution 3.0 (CC BY 3.0)
Copyright ○Figure 5: Ion density distribution at t = 25 µs.