Modeling process of the neutral beam re-ionization loss

CPC(HEP & NP), 2010, 34(7): 972- 977Chinese Physics CVol. 34, No. 7，Jul, 2010Modeling process of the neutral beamre-ionization lossLIANG Li-Zhen(梁立振) HU Chun- Dong(胡纯栋) XIE Yuan: Lai(谢远来)XIE Ya-Hong(谢亚红) NBI Team(NBI组)Institute of Plasma Physics, Chinese Academy of Sciences, Hefei 230031, ChinaAbstract The basic process of re-ionization loss was studied. In the drift duct there are three processesleading to re-ionization loss: the collision of neutral beam particles with the molecules of background gas,similar collisions with released molecules from the inner wall of the drift duct and the ferrt-collisions amongparticles with diferent energy of the neutral beam. Mathematical models have been developed and takingEAST-NBI parameters as an example, the re ionization loss was obtained within these models. The resultindicated that in the early stage of the neutral beam injector operation the released gas was quite abundant.The amount of re-ionization loss owing to the released gas can be as high as 60%. In the case of a long-timeoperation of the neutral beam injector, the total re-ionization loss decreases from 13.7% to 5.7%. Then the re-ionization loss originating mainly from the collisions between particles of the neutral beam and the backgroundmolecules is dominant, covering about 92% of the total re-ionization loss. The drift duct pressure was thedecisive factor for neutral beam re-ionization loss.Key words Re-ionization loss, background molecule, ferret-collision, excitation outlet, thermal outgassingPACS 52.50.Gj1 Introductionfore the key issue is how to reduce the re ionizationloss of a neutral beam, which is even more importantthan increasing the energy of its particles.For the majority of the NBI, it is dificult to mea-which is envisaged for heating fusion plasma to igni-tion temperatures. A neutral beam current drive hassure the re-ionization loss accurately. In this articlebeen observed in most large Tokamaks [1, 2]. Heat-three of the basic processes of re-ionization loss areing with a neutral beam is a complex process. Thdiscussed and the corresponding mathematical mod-ions must first be produced and accelerated to theels are developed. Taking a hydrogen neutral beamrequired energy. Then they are neutralized by chargewith the EAST-NBI engineering parameters as an ex-exchange in a gas target and the unwanted residualample [3], the re-ionization loss will be derived withinions removed. Neutral atoms injected into a plasmathese mathematical models.travel in straight lines, being unffected by the mag-netic field.2 Collisions model for re- ionizationUnder neutral beam re-ionization loss one under-particles of the neutral beam and the background gasneutral beam. Atoms of a neutral beam impact back-in the drift duct. Because of the stray magnetic fieldground molecules, when the neutral beam is pass-of a Tokamak, neutral beam re ionization loss noting through the drift duct. Most of the backgroundonly affects the working efficiency of the beam, bumolecules are molecular hydrogen. It is obvious thatalso can damage the device to some extend. There-the collision in the drift duct is between neutral par-Received 29 July 2009* Supported by National Science Foundation Project (10875146, 10575105) and Ch中国煤化工’wledge Inno-vation Project: the Study of Neutral Beam Steady- State Operation of the Key Techr1) E-mail: lzliang@ipp.ac.cnYH| CNMHG⑥2009 Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy ot Sciences and the Instituteof Modern Physics of the Chinese Academy of Sciences and IOP Publishing LtdNo. 7LIANG Li-Zhen et al: Modeling process of the neutral beam re-ionization loss973ticles. Therefore, the following collision model mayrelativity, a modified quantity can be used insteadbe established for collision process.The collision model includes two particles ear-2mvx c+(1-")r3)marked by A and B with the radius of R，R2. The .mass and speed of the two particles are m1, m2, V1, V2in the neutral beam, U is the speed of the atoms inrespectively, hydrogen atoms have high-speed direc-the neutral beam (determined by the beam energy),tional movement and background molecular hydrogenc is the speed of light in vacuum and RH is the radiushas random thermal motion. Therefore, the follow-of the hydrogen atoms. The probability of the colli-ing assumption is reasonable, v1=v=√, v2=0sions between the particles of the neutral beam andWhere, Ep is the energy of particles of neutral beam.the background molecules can be written as follows:After collision, the speed of two particles are v(hx"+(1-")Ru +Ru06 and the angles with V1 are a, β respectively. Fig. 14)shows the structure of the collision model. Thus, the3「RT\2collision probability for this process could written asPNA ,r(Rr+R2)(1)where，RH2 is the radius of a hydrogen molecule.Thus, if the length of the drift duct is l, the re-where, S is the cross section of collision space.ionization loss resulting from collisions with the back-ground gas may be expressed ass\lm(.x"+(1-")Ru+R2) PNA\5)mRTOn the assumption that single charge particlesconstitute the beam in the accelerator system, theFig. 1. Structure of collision model.number of electrons gained from re-ionization can ap-proximately be expressed as3 Re-ionization loss resulting from co-llisions with background moleculesm(x*+(1-")Ra+Ru2) PNs\ 2mvItnDuring the working process of a neutral beam,the time sequence of gas input for the neutralizer andwhere, I is the beam current, t is the neutral beamthe ion source occurs always before the start time ofpulse length, e is the elementary charge and η is thethe high voltage. Thus, there are many backgroundefficiency of the neutralization process.molecules when the neutral beam is passing throughthe drift duct. After the removal of the residual ions4 Re-ionization loss resulting fromthe neutral beam is composed of hydrogen atoms withcollisions with released moleculesthree energy components一full energy, half energyand 1/3 energy [2, 3]. Generally speaking, there is noUnder the powerful magnetic field of a Tokamakcoulomb effect during the collisions in the drift duct.the ions and electrons resulting from re ionizationAssuming that the background gas is a uniformlystrike the wall of the drift duct. Generally the in-distributed ideal gas of pressure P, one can derive thener wall of the drift duct is covered by metallic 0x-volume of its molecules from the equation of state:ide. Thus, the excitation outlet and the thermal out-VH2 =2)gassing occur during the passage of the neutral beamNAPthrough the drift duct.where, R is the gas constant, T is the temperature ofThe ratio of the cross section of oxide node and thethe background gas and Na is the Avogadro constant.area of the oxide crystal lattice is about 0.04- 0.06 and .Generally the energy of hydrogen atoms amounts tothe probability of the interaction between the electrondozens of keV, which is much higher than the ion-and the oxide node中国煤化工e ion-ization energy. The characteristic dimension of theization probability.[HCN MH Gactionparticle size is not its diameter, but the de Brogliebetween the ions and Iu iouppuoud to bewave length [4- 6]. According to the special theory of1 [7]. For stainless steel the cofficient of the excita-974Chinese Physics C (HEP & NP)Vol. 34tion outlet by electrons 7Yex = 0.004- 0.03, for the ionsFor a given cross section of the drift duct and a shortit is 7; = 0.04-0.06. Also during the operation periodenough time such as to keep all molecular oxygen inheat is absorbed by the wall of the drift duct. Thisthe drift duct, the volume of the molecular oxygen isthermic energy leads to outgassing. However, sincegiven by:the drift duct is full of hydrogen, molecular hydrogenVo2 =could be the exclusive gas obtained from the thermalSoutgassing. The experimental results indicated thatthe amount of the excitation outlet is ten times thatm(.x.+(1-")Ru+Rua ) PN、of the thermal outgassing [7].Take 0.05 as the coefficient of the excitation out-RT20e(8let for stainless steel. Thus, the number of oxygenmolecules is given bySo, the re-ionization resulting from the collisionsn(x.+(1- "Rn+Rm2 ) PNAbetween the neutral beam particles and molecular“2mv^ CItnoxygen can be expressed asx 20(7) 」( 2mx"+(1-")Ru+Ro2) (( amnx"+(1- ")R+ Ru) IPN.Itn2mv .2mv(9)20eSRTSimilarly, the molecular hydrogen from the ther-I energy and the particle with the half energy, the par-mal outgassing will lead to the re- ionization lossticle with the full energy and the particle with ththird energy. In the case of a uniformity distribution,.x.+(1-")Ra+ Ru2) IPN,Itnthe volume occupied by the particles with differentn(2mox200eSRTenergy is given by10)Sp5 Re-ionization loss resulting fromv,= Sgutm/2Ep Sge(11)nm IT;ferret-collisionswhere, Sg is the cross section of the neutral beam; .ions have been removed by the bending system, the i= 1,2,3 denotes the particles belonging to the groupsenergy of the atoms in the neutral beam is dividedwith full energy, half energy and one third energy re-into three groupsspectively, 7i is the corresponding fraction of the par-third of the full energy. So, as some particles withticles and n is the number of the particles.the half energy pull up to the particles with the thirdAccording to the above analysis, the rate of ferret-energy, the ferret-collision will happen. Similarly, thecollisions moving particles from group2 to 3 is givenferret-collision happens to the particle with the fullbyh+(1-)Rm+mx些+(1-号)Ru23 =(12)2E Sgem Iγ3Thus, the re-ionization loss resulting from the corresponding ferrt-collision can be expressed asr|。-x+(1-号)Ra+bx字+(中国煤化工7/23 =_2mv3^2mv2:MYHCNM HG(13)No. 7LIANG Li-Zhen et al: Modeling process of the neutral beam re-ionization loss975Similarly, the other two re-ionization losses resulting from the ferret-collision are given byx告+(1- =)n,h -x≌+(1-丝)|l“|2mvnx712(14)/2E SgeVmI7:bmx出+(1-号)+mx次+(1-架)Rh_、“|2mv7/13 =21001mU3(15)V mIrsbeam passes through. The duct pressure shows a slow,6 Calculations and discussionalmost linear, rise with time during the heating injec-tion [8]. If the pressure in the duct is increased to P2From experiments it is known that there is a dy-from P1, the length of the drift duct isl. So, 7B, 7h,namicpressure in the drift duct when the neutral| 7e would be modified by an integral as shown below(hx"+(1-")Ru+RuVA“2muP2- P1-|(p+P7Pr)d",(16)7hmr2((nx"+(1- ")Run+Ru2) N.Itn |pr+P2=Pl )dl'，(17)200eSRT(hx"+(1-")Rn+Ro2) (.x"+(1-")Ru+Rm2)j NxItn( 2mvYem =20eSRT(pr+?二Pr)d(18)For a long pulse or an enduring NBI the molecules will be pumped out in a time T, which is much shorterthan the pulse length. We define this as the characteristic time of the pump. In this case only part of themolecules will contribute to the re-ionization and our equations have to be adjusted accordingly.|π- hxy.hx"+(1- ")Rn+Rm2) NAtn'g( mx+(1-号)Ru+Ros )( 2moxpn+R=Pr)dlJ\'(tr);| π2(x"+(1-")R+R2) N\Itn(pr+P2=PIr)dl' (t 论文截图