Review on Space Charge Compensation in Low Energy Beam Transportation

ZHANG Ailin， PENG Shixiang， REN Haitao， ZHANG Tao，ZHANG Jingfeng， XU Yuan， WEN Jiamei， WU Wenbin，GUO Zhiyu， CHEN Jiaer

（1.State Key Laboratory of Nuclear Physics and Technology ＆Institute of Heavy Ion Physics，School of Physics，Peking University，Beijing 100871，China；2.University of Chinese Academy of Sciences，Beijing 100049，China）

Review on Space Charge Compensation in Low Energy Beam Transportation

ZHANG Ai－lin1，2， PENG Shi－xiang1， REN Hai－tao1， ZHANG Tao1，ZHANG Jing－feng1， XU Yuan1， WEN Jia－mei1， WU Wen－bin1，GUO Zhi－yu1， CHEN Jia－er1，2

（1.State Key Laboratory of Nuclear Physics and Technology ＆Institute of Heavy Ion Physics，School of Physics，Peking University，Beijing 100871，China；2.University of Chinese Academy of Sciences，Beijing 100049，China）

Demands of high intensity accelerators are increasing for fundamental science research and engineering applications.In such kinds of accelerators，the beam in low energy parts is space charge dominated.This can result in large and irreversible emittance growth.Space charge compensation which occurs by tapping opposite polarity of the particle of the beam is a helpful way to overcome the effect caused by the space charge.An extended particle in cell（PIC）code jointed with the Monte Carlo collision（MCC）has been developed in Peking University（PKU）for modeling the space charge compensation.In the meantime，experiments of low energy H＋and H－ion beam have been carried out.The results of the numerical simulation agree well with the experiment ones for both H＋beam［1］and H－beam［2］.Details will be presented in this paper.

high intensity accelerators；low energy parts；space charge effect；space charge compensation；PIC－MCC

Classification No：O57Document code：APaper No：1001－2443（2016）03－0205－09

Introduction

High power accelerators can give rise to a large variety of scientific applications，used for both fundamental research and application research.Several projects of high current accelerator have been built and are now in commissioning or operational phases，such as the spallation neutron sources（SNS［3］，CSNS［4］，and ESS［5］），the muons factories（J－PARC［6］，and ISIS［7］），the radioactive ion beams production（FAIR［8］，and SPIRAL2［9］），the international fusion materials irradiation facility（IFMIF）［10］，and accelerator driven sub－critical system（ADS）［11］.Space charge effect and space charge compensation are important issues along the whole high intensity accelerators.In high energy case，space charge induced tune shift and beam stabilization.In low energy section，the beam is space charge dominated which can result in large and irreversible emittance growth.Such a beam usually need space charge compensation to control the space charge effect.

The space charge compensation occurred by tapping opposite polarity of the particles could come from the

secondary particles produced by gas ionization or supplied by specific device.For gas ionization，it takes time for a particle of the beam to produce a neutralizing particle on the gas.It is expressed as， whereσiis the ionization cross section of the incoming particles on the gas and ngis the gas density in the beam line.The gas space charge compensation only applies to those beam whose pulse length is longer thanτ，for example CW beam or long－pulse beam.For those short pulsed beam，the opposite polarity of the particles should be initiatively provided and sustained by specific device without transient time limit，such as Electron Volume［12］and Gabor Lens［13］.In this paper，we will focus on the space charge effect and space charge compensation of CW beam and long－pulse beam.

Study on space charge compensation can help us to understand the processes during the compensation and guide accelerator design.Experiment research as well as numerical simulation are complementary ways on this study.To simulate the process of space charge compensation within an ion beam，the space charge effect should be treated by taking into account either through a linear analytical model or by treating the beam fully three－dimensional through particle－in－cell（PIC）methods.At PKU，a Monte Carlo collision （MCC）［14］package including the null collision method has been developed as an addition to the usual PIC charged particle scheme.This PIC－MCC code done with 2DMATLAB code has been used to simulate the space charge compensation of H＋beam.The simulation results had a good agreement with the experimental ones when dealing with Ar compensating H＋beam［1］.Recently，this PIC－MCC simulation code was improved to 3Dmodel and had been used in the H－beam after considering the difference of positive and negative ion beams［2］.Again，the results obtained by H－beam experiment were coincident well with the numerical results.Space charge effect and space charge compensation，and experiment and simulation of space charge compensation will be presented in the paper.

1 Space charge effect

Space charge is the most fundamental of the collective effects whose impact generally is proportional to the beam intensity.The defocusing force of space charge effect will lead to emittance growth（εrms）［14］.It can be expressed by the generalized perveance K，

Here Xis the position of the ions in the beam，ΔWnlis the normalized non－linear field energy which is mainly determined by the density distribution of the ion beam.The generalized perveance，a dimensionless parameter K，is defined as，

The perveance Krefers to the magnitude of space－charge effects in a beam，and it will largely determine the particle trajectories in drift region.In equation（3），Iis the density of the beam，while we approximate thatΔWnl∝I，from equation（1）we getΔεrms∝I，which means the emittance growth is proportional to beam current.

Figure 1showed the perveance Kunder different energy in several high current projects［15］.As shown in Fig.1，in low energy region（100keV）the perveance Kis 5×10－3，five orders higher than that in the high energy region（100MeV）.From equation（1）we know thatΔεrmsis proportional to.This means the emittance growthΔεrmscaused by space charge effect in low energy is hundreds times larger than it in the high energy region.Therefore the following discussion will focus on the low energy part of accelerator.

Low energy beam transportation（LEBT）is a beamline that connects ion source and the acceleratingstructure whose energy is usually tens kV to hundreds kV.Emmitance growth will be the significant problem according to Figure 1and equation（2）.The space charge in LEBT of the high intensity accelerators should be compensated carefully.

Figure 1 The perveance K under different energy in several projects［15］

2　Space charge compensation

The most common way for space charge compensation in low energy parts of accelerator is gas ionization，and the gas could come from residual gas or initiatively injecting.Figure 2is an example［16］.When a proton beam is propagating through the gas of the beam line，the proton beam will ionize the molecules of residual gas or injected gas within the vacuum pipe，the electrons will be absorbed to the beam core while the ions are expelled from the beam core，this results that the beam will be neutralized，it’s so called space charge compensation.

Figure 2 Proton beam compensated with gas ionization［16］

The space charge compensation can be particularly different from each other under different electromagnetic environment.The ions that generated within an ion source body are formed as an ion beam through a beam extraction system.When an extraction electric field applied on the ion source，the wanted sign particles will be extracted from the plasma while the opposite charge particles will be decelerated and reflected towards the plasma.To avoid the compensating particles lost towards the ion source，an acceldecel extraction system has to be used in GSI［17］.The experimentally observed beam profiles using viewing targets and the simulation using the three－dimensional 3Dsimulation code KOBRA3－INP［18］have a good agreement.Figure 3showed a simulation result concentrating on magnetic field line and extraction aperture from KOBRA3－INP.

Once the beam is extracted from the ion source，it has to be transported and matched by the lowenergy beam transportation（LEBT）to the first accelerating structure such as a RFQ.The focus can be done with electrostatic or magnetic elements［19］.

Figure 3 Magnetic field lines going on different radius through the extraction aperture：1mm，2mm，and 6mm［18］

Electrostatic LEBT mainly consists of axisymmetric electrostatic focusing components.These lenses are affecting the beams by the electric field they generated so to adjust the beam transmission parameters to achieve the goal of matching the beam emittance with the cavity acceptance.The electrostatic LEBT is compatible with fast beam chopping as there is no transient time for the space charge compensation.The beam is propagating in electrostatic LEBT without any space charge compensation because the neutralizing particles are repelled by the electric field induced by the focusing elements.The injector developed by PKU for the DWA（Dielectric Wall Accelerator）［20］is a typical electrostatic injector，which consists of an ion source and a 20cm six electrodes LEBT.The SNS（Spallation Neutron Source）injector shown in Figure 4 is composed by an H－ion source with a 12cm long electrostatic LEBT equipped with two Einzel lenses.

Nowadays，it is commonly accepted that an optimal LEBT for high current accelerator applications consists of focusing solenoids with space charge compensation.Such magnetic LEBT is spark free and low sensibility to beam loss，and beam diagnostics and mass separation can be easily inserted.However，the pulse rise time in magnetic LEBT which is dominated by the transient time of the space charge compensation should be no shorter than hundreds of s.Two－solenoid Magnetic LEBTs have been successfully used for high current（＞100mA）proton beam［22－24］.Figure 5showed a schematic view of the designed two－solenoid magnetic LEBT in SNS.It consists of solenoids S1and S2that focus the H－beam into the RFQ entrance at the right，separated by 50cm used for pumping and beam diagnostics.

Figure 4 The electrostatic LEBT of SNS［21］

The constellation effect of the beam maybe lead to instability in anywhere the space charge compensation occurs.The partial space charge compensation can be unstable because of the nonlinear fluctuating electric fields created by complex motion of compensating particles（electrons and ions）in the beam＇s potential well［25］.The strong beam instability connected with secondary particle oscillations in the beam potential was observed and described in［26，27］.A first theory of this instability was developed by Chirikov［28］and a kinetic description with quadrupole oscillations was presented in［25］.Reviews with further development in this field，named now e－p instability（or electron cloud effect）were presentedin［30－32］.Now this instability is a main limiting factor of beam performance in the Large Hadron Collider （LHC）in CERN，including some beam transfer lines and in many other accelerators and storage rings［30，32］.

3　Simulation for space charge compensation

Simulation codes can take space charge compensation into account either by a linear analytical model （as for example presented in Reiser［33］）or by treating the beam fully three－dimensional through numerical simulation methods［1］.The original analytical formula about space charge compensation was presented in 1968by Nezlin M V［34］.Then，in 1977Gabovich published a detailed review article on the processes involved in compensation and decompensation of positive and negative high intensity ion beams considering dynamic and decompensation of the ion beams as well as collective processes in the beam plasma［35］.With the development of computer technology，numerical simulation becomes more and more reliable.Numerical simulation codes for space charge compensation had been developed in many labs，such as WARP［36］developed in Lawrence Berkeley National Laboratory（LNBL），SOLMAXP［37］developed at CEA／ Saclay，and IBSimu［38］3Dsimulation code developed at CERN.However，the collisions in those codes are not calculated accurately enough.At PKU，a PIC－MCC code concentrated on collisions had been developed in PKU.Beam loss and instability caused by collisions were carefully treated within this code.Its scheme of PIC－MCC simulation is shown in Figure 6.This is similar to the input／output routines of any other numerical tool.

Figure 5 The two－solenoid magnetic electrostatic LEBT of SNS［24］

Figure 6 Scheme of the PIC－MCC simulation in PKU

In order to verify the PIC－MCC model，experiments were performed on PKU Ion Source Test Bench.Figure 7is a photo of this bench［39］.It consists of a set of microwave system，the permanent magnet 2.45GHz ECR ion source，a tri－electrode extraction system，and a beam diagnostic section with a Faraday Cup（FC1）that integrates a set of slit－grid emittance measurement device.Compensation gas is injected in the same section of FC1.Mass Flow Controller was used to control the compensation gas flow.

4　Comparison of experimental results and simulation ones on space charge compensation

4.1H＋beam results

The PIC－MCC model for H＋beam concentrates on the scattering effect which can cause particle loss.Experiment of the space charge compensation using Ar in H＋beams is presented in this paper.Ion beamswere transported through 300mm of drift section under various vacuum conditions.The simulation result is shown in Figure 8.Comparisons between the 2DPIC－MCC simulations（Figure.9）and the experiment showed the numerical results had a good agreement with the experiment.By studying the scattering effect，we found out an appropriate compensation circumstance to get the best efficiency in Low－energy Beam Transport.

Figure 7 Skeleton diagram of PKU ion source test bench［39］

Figure 8 2Dsimulation result for H＋beam（compensate with 0.05sccm Ar）

Figure 9 Current（left）and emittance（right）comparison between experiment and simulation for H＋beam

4.1H－beam results

The 2DPIC－MCC was improved to simulate the space charge compensation of H－beam in PKU.The biggest difference between compensation of positive and negative ion beams are the masses of the electrons and ions produced by gas ionization.In a negative ion beam，the space charge effect is neutralized by heavy positive ions while positive beam is neutralized by light electrons.The results are that the negative beammaybe overcompensated because the ion is harder to be moved than the electrons.Experiments were done at PKU ion source test bench.Compensation gas He and Ar were injected directly into the beam transport region to modify the space charge compensation degree.The 2DPIC－MCC was improved to a 3DMATLAB PIC－MCC code.Figure 10showed an example of the 3Dsimulation result of H－beam transport 50mm to faraday cup.In this case，the beam focal point，the electron temperature is 10.8eV，the max electron density on axis is about 5.8×1015m－3，the Debye length is about 1.7mm and the plasma frequency is about 2.7GHz.

Figure 10 Simulation for H－beam transport 50mm to faraday cup

Figure 11 Simulation and experiment comparison on current and ratio for H－beam

Figure 12 Simulation and experiment comparison on emittance for H－beam.The minimum emittance is the cation where it is believed the space charge compensation is optimum.For He 4sccm，while for Ar is 0.6sccm.

Figure 11showed that the simulation results of current of H－and ratio of H－to total beam current have good agreement with the experimental ones.Emittances are calculated and compared in Figure 12.Both He and Ar can reduce the space charge effect in H－beam transportation.However，to get the bestemittance result more than 6times He inflow（4sccm）is needed than Ar（0.6sccm）.The simulation results agree well with the experiments and it will help us to find a good compensation circumstance to avoid the decompensation and overcompensation region in H－beam.

5　Summary

In this paper we reviewed the space charge compensation in LEBT.Until now，the beam dynamics simulations of LEBTs have been done with particle tracking codes.The PIC－MCC code developed in PKU had been used to model the space charge compensation，and it has a good agreement with the experiment which was performed on PKU ion source test bench.The simulation result agrees well with the experiments.That helps us to understand the process during the compensation in H＋beam and H－beam，and guides us to find a good compensation circumstance to improve the transmission efficiency for LEBT.It has been demonstrated that numerical simulation code PIC－MCC developed in PKU can be used for injectors design of high intensity accelerators.

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低能傳輸段空間電荷補(bǔ)償效應(yīng)

張艾霖1，2， 彭士香1， 任海濤1， 張 滔1， 張景豐1，徐 源1， 溫佳美1， 武文斌1， 郭之虞1， 陳佳洱1，2

（1.北京大學(xué)物理學(xué)院核科學(xué)與核技術(shù)國(guó)家重點(diǎn)實(shí)驗(yàn)室＆重離子物理研究所，北京 100871；2.中國(guó)科學(xué)院大學(xué)物理科學(xué)學(xué)院，北京 10049）

近些年來(lái)，隨著基礎(chǔ)科學(xué)和應(yīng)用科學(xué)對(duì)強(qiáng)流加速器需求的日益增加，強(qiáng)流加速器得到了很大推廣和發(fā)展.在強(qiáng)流加速器的低能段，空間電荷效應(yīng)會(huì)導(dǎo)致束流發(fā)射度的增長(zhǎng)，束流品質(zhì)的變壞.這樣的束流通常需要空間電荷補(bǔ)償來(lái)控制空間電荷效應(yīng).空間電荷補(bǔ)償是指束流可以通過(guò)吸收與束流電性相反的粒子從而減少束流空間電荷發(fā)散力的一種效應(yīng).北京大學(xué)自主開(kāi)放了PIC－MCC空間電荷補(bǔ)償模型，該模型被應(yīng)用在H＋和H－束流的空間電荷補(bǔ)償模擬當(dāng)中，且得到了與實(shí)驗(yàn)符合得比較好的結(jié)果.

強(qiáng)流加速器；低能束流傳輸段；空間電荷效應(yīng)；空間電荷補(bǔ)償；PIC－MCC

10.14182／J.cnki.1001－2443.2016.03.001

date：2016－03－20

Supported by the National Natural Science Foundation of China（11575013，11305004）.

Author＇s brief：ZHANG Ailin（1989－），male，born in Wanzhou District，Chongqing，PhD student.Research interests：high intensity CW ECR ion source，space charge compensation，beam diagnosis；PENG Shixiang（1966－），female，born in Ningguo city，Anhui Province，doctor，doctoral tutor，the alumna who graduated in 1986from Physics Department of Anhui Normal University.Research interests：high intensity high brightness ion source，high current low energy beam transport，beam diagnostio.

引用格式：張艾霖，彭士香，任海濤，等.低能傳輸段空間電荷補(bǔ)償效應(yīng)［J］.安徽師范大學(xué)學(xué)報(bào)：自然科學(xué)版，2016，39（3）：205－213.