Budker Institute of Nuclear Physics, SB RAS, Novosibirsk, Russia

The electrostatic tandem-accelerator with vacuum insulation is under development in frames of the project of creation of neutron source for neutron capture therapy of cancerous tumors [1]. It is designed for proton energy up to 2.5 MeV and beam current up to 40 mA (Fig. 1). One of the parts is the target, which converts negative hydrogen ions accelerated to half of the total energy into protons. The target in solid, liquid or gaseous state should satisfy the following requirements:

1. It should provide 98 – 99 % stripping of hydrogen negative ions beam with energy from 0.96 to 1.25 MeV into protons.

2. It should not lead to proton spectrum widening more than by 2 keV.

3. The vacuum deterioration in accelerating gap should not cause neither decrease of electrical strength of vacuum gap nor the potential redistribution on the electrodes of accelerating gap by the additional current on the electrodes. It is considered [2], that 10^–5 torr pressure ensures the high voltage strength of accelerating gaps, but 10^–4 torr pressure degrades the tandem operation reliability because of the breakdowns of high voltage vacuum gaps.

4. The preliminary numerical simulations of cold H^- beam transportation show that the use of magnetic or electrostatic decelerating lens before the tandem entrance allows to transport 25 mA beam 6 mm in diameter through 400 mm length in the target region. Therefore the aperture of stripping target should be more than 6 mm.

The analysis of targets of different types for application in accelerator-tandem is given in this work. The gas flow regimes from the stripping tube and the estimations of gas density in accelerating tract are considered. The possibility to pump the target gas by outer pump and pump placed directly inside the high voltage electrode are investigated. The effects of ion beam and target gas interaction are considered. The analysis of thermal regimes of stripping tube is made. The program of the following experiments is defined.

The graphite foil of 0.1? 1 m m thickness is usually used as a stripper for H^- ions with energy higher than 400 MeV and current ~ 0.1 mA. At an achieved foil temperature 900 ° K the saturated vapors pressure is very low, less than 10^–10 torr [3], so the lifetime of the target is several weeks [4]. For passage of 1 MeV 40 mA beam 10 mm in diameter through 1 m m graphite foil the ionizing energy losses are 40 keV [5], and foil without forced cooling is heated up to 3800 K temperature with corresponding increase of saturated vapors pressure up to 10 torr [3]. Big energy spread of ion beam after stripping, limited lifetime of the foil and big pressure of saturated vapors at high temperature does not allow to use graphite foil as a stripper.

A big experience in dealing with liquid lithium has been accumulated at BINP [1, 7, 8]. The velocity of liquid lithium jet target 1 m m thick and 10 mm wide flowing perpendicular to the accelerated ion beam should be more than 100 m/s taking into account the maximum allowed temperature of lithium 320 K when the saturated vapors pressure reaches 10^-5 torr value. It is achievable. The lithium jet heating by the beam results in change of flow regime in jet and decrease of jet density. It is proposed that application of jet as a stripping target will be considered after planned experiments with liquid lithium neutron producing thick jet and after numerical simulations in hydrodynamical approximation.

It is possible to use the transversal sonic or supersonic metal steam jets with circulation [9, 10] as a stripping targets with big acceptance. In this case a steam condensed into liquid is pumped to the heater on the output of a nozzle. The mercury vapors coming from the stripping target can be pumped by cryogenic pump. The use of mercury requires the additional safety measures to be undertaken and the use of lithium proposes checking of the vacuum gaps breakdown strength conservation.

For stripping of H^- ions with 1 MeV energy into protons any gaseous target is suitable, practically, because it allows almost 100 % beam conversion into protons [12, 9, 23]. The corresponding data about cross-sections and equilibrium protons output is given in Table 1

Gases mentioned in two last strings of Table 1 require some comments. The fact is that geometrically all diatomic and most part of triatomic molecules are linear. Therefore fast incident particle interacts effectively only with one of the atoms, because the probability of molecule orientation along the trajectory of fast incident particle is very small. The probability of interaction during collision of fast particle with polyatomic space-structured molecule such as CCl₂F₂ or SF₄, is weakly dependent on molecule orientation. Therefore not numerous experimental data [23] indicate the significant excess of their stripping cross-sections over the ones for di- and tri- atomic molecules.

We suppose that stripping cross-sections on the other compact space-structured molecules, halogenides, TaBr₅, SF₅, SF₆, containing more than 5 atoms of halogen, will be more by 20 – 40 % than for SF₄. Besides the big stripping cross-section such molecules are attractive by the fact that atoms capable to release in solid phase are well hidden in the molecule depth. Because the products of dissociation of the main molecule – halogen atoms and halogenides of lower kind are in general volatile the appearance of solid sediment will be minimal. At the same time the exoticism of application of such a target doesn't allow to choose it without preliminary experiments.

Physically, the target is a cylindrical pipe with gas input in the middle. During beam passage through the target the charge-composition of the beam is being changed. The typical dependence of beam charge-composition vs. target thickness is given in Fig. 2, and the protons yield is given in Table 2.

Let us consider argon gas stripping target. It's choice is conditioned on the fact that argon is a rare gas and, that's the most important, because the stripping is not accompanied by dissociation leading to undesirable heating and appearance of interfering dissociation products.

For 99% beam stripping the linear thickness of the argon gas target L = 3,1 ? 10¹⁶ cm^–2 is necessary. It corresponds to the average pressure p = <nL>kT/L, the practical expression for which at a room temperature looks enough simple as:

<P> [Torr] = 0,94 L^–1 [cm]. For example, for the stripping tube with L = 40 cm the average pressure <P> = 2,3 ? 10^–2 Torr. In the considered tube length range of 20 – 40 cm the free path l > L/375 is more than 0,5 mm. It's considered [14, 15], that for free path of molecules l < 0,01 D, where D — tube diameter, the viscous flow regime is realized and for l > 0,33 D — molecular, when molecules move free without noticing each other, colliding with the walls of tube and reflecting from them. For 0,01 D < l < 0,33 D the intermediate flow regime has place. In given case for tube of 40 cm length and 10 mm in diameter the free path is l ? 0,1 D, so in the center of the tube the intermediate flow regime is realized, while on the tube ends – the molecular one.

Let us estimate the gas flow in molecular regime. The tube conductance is defined as U_m [l/s] ~ 10 a D³ L^–1 [15], where all dimensions are in centimeters, and a – Clausing coefficient, which takes into account the reduction of conductance due to flow before the tube input and flow after exiting the tube. It depends on relation L/D and in given case it's equal to 0,91. However, owing to gas input into the tube directly, a must be taken bigger, so for the upper estimation a = 1 will be considered. Because gas is inputted in the middle of the tube and flows out through both ends, the gas flow is defined as Q = 2 P₀ U, where conductance U is defined on the length two times less than one of the stripping tube, and P₀ – is the pressure in the middle, which is two times bigger than the average one <P>, because pressure is distributed along the tube linearly [16]. Then the gas flow is Q = 46 mTorr l/s. Numerical simulation undertaken using test particles method without taking into account their collisions with each other gives the 1.6 times less gas flow.

Let's take into account the influence of intermediate gas flow mode. The conductance U_mv can be expressed through itself in molecular mode U in the form convenient for comparison [17]:

U_mv = U (0,074 + z ) = U (14 + z ),

The gas flow can be reduced by 1.6 times, if one allows 95 % beam stripping, the reduction occurs owing to both pressure decrease and approaching the flow regime to molecular one. In addition the gas flow can be reduced twice as it was shown in [1], using the special form of the internal surface of the stripping tube. One can see that the operation regime with 20 mTorr l/s gas flow from the stripping tube can be expected. The value of this gas flow is yet comparable with gassing from the surface of electrodes.

To sum up let write the expression for gas flow of any gas in our parameters range and pay attention to its dependence on length and diameter of the striping tube.

,

where gas flow Q is expressed in l Torr/s, all dimensions are in centimeters, temperature T in Kelvin degrees, M – molecular mass. In order to decrease the gas flow it's necessary to tend to reduce diameter and increase the tube length to realize the molecular flow regime. The realization of flow regime close to viscous is undesirable due to the following effect too. Beam stripping leads to significant gas heating. And if in non-collisional regime the heating of separate molecules can be easily removed by cooling the stripping tube because hot molecule quickly hits the tube wall and transmits the most part of it's energy to it, but in viscous, collisional mode as it's well known [18, 19], the heating of sub-sonic jet leads to its acceleration and density decrease that will demand the bigger gas flow.

Let us determine the pressure inside the central electrode of the accelerator with 7 intermediate electrodes (See Fig. 1) at a high pumping rate of the external pumps. The hole 20 cm in diameter in the high voltage electrode provides the conductance 3000 l/s and can be increased by increasing its diameter. The holes in other 7 electrodes, made as covers with diameter not less than 50 cm, raised a little by 4 cm provide the conductance 6000 l/s. If these holes 50 cm in diameter are made as a jalousie or sectors than the conductance will be increased to 12000 l/s. One can see that conductance through the electrodes with holes installed in series can be got on level 1500 l/s. Therefore, pressure inside high voltage electrode can be 3,5 ? 10^–5 Torr at a gas flux 55 mTorr l/s, that is admissible.

So, if it would be possible to transport the beam less than 10 mm in diameter on 400 mm length, in this case the use of the argon gas target would be allowable and attractive by the simplicity of realization.

The simulation of stripping target gas behavior

The gas flow from the stripping tube were simulated by test particles method with number of particles up to 10⁴. The initial direction of particle motion of each particles and direction of particle reflection from the surface were assigned in a random way with probability proportional to cosine of the angle with normal to the surface. The particle collisions were not taken into account.

In Fig. 4 three angle distributions of particle flux are given. The flux indicatrix are plotted in coordinates N/(q )/N, q ; where N/(q ) = D N (2p sinq D q )^–1 – molecular flux into unit spatial angle in direction q with respect to the tube axis; N – total molecular flux, coming out from the tube end. The distribution of a in Fig. 4 performs the calculation results in non-collisional case. However, because free path is much less than the tube length such approximation is not applicable and calculations results can be only the estimation of gas flux forward along the beam axis. Big gas flux in forward direction is formed because particles in this direction fly from the whole tube including big gas density region in its center. The collisions in the tube change the distribution, anyhow they reduce gas forward flux. b distribution in Fig. 4 corresponds to the calculations in case when the tube length is of the order of free path. In order to take into account particle collisions their source in calculations was like circle – cross section of the pipe cut on the distance 2 cm from its end. The ultimate distribution c in Fig. 4 corresponds to viscous gas flow mode along the whole tube, when the distribution of molecules flying from the tube into unit spatial angle is proportional to cosine of the angle between tube axis and molecules fly out direction.

In Fig. 5 the graphs of pressure dependence in the hole of high voltage electrode and reference part of gas consumed which hits directly the hole 2 cm in diameter from the stripping tube are shown. They are drawn versus distance between tube end and hole in electrode.

The particle motion simulation in non-collisional approximation inside the high voltage electrode is correct, because of low gas pressure. The calculations have shown that the most effective way to reduce gas flux to accelerating gap is placing of two diaphragms on distance of the order of diameter of the hole in electrode D (Fig. 6). The diameters of holes in diaphragms are equal to the stripping tube diameter and less than D. The use of diaphragms allows to reduce gas flux to inter-electrode space caused by many times reflected particles down to 20 % of the direct flow from the stripping tube. To avoid direct visibility of the cold surface of nitrogen pump from the beam side special screens like half of cylinder and cone are installed. Gas sorbed by the pump is distributed on its cold surface uniformly enough.

The attendant effects of ion beam interaction with gas molecules of the stripping target.

Let us consider the effects of ion beam interaction with target molecules on example of well investigated charge-exchange process on nitrogen molecules.

Ionization losses of 1 MeV ion during stripping on nitrogen molecules are 275 eV [1] and result in 11 W loss of 40 mA beam. For the molecular gas flow mode the energy released is carried by molecules or atoms, which take part directly in the stripping event, to the stripping tube. For viscous gas flow regime energy is transmitted by thermal conductivity. The stripping of H^– ion into proton is accompanied by the appearance of 2 electrons with velocity equal to one of fast ion. The power of 500 eV electrons dissipated in target is 40 W. It is transmitted to the wall of stripping tube by means of electron heat conductivity. The heating power caused by Rutherford scattering is of the order of 10 W.

So, the total power of energy losses in the stripping target is 60 W and is mainly transported to the wall of stripping tube.

The similar process of fast ions stripping accompanied by the appearance of atoms, protons, electrons and energy losses have place in the acceleration tract too. Although residual gas density is much less the one of the stripper the stream of electrons, ions accelerated in electric field together with fast neutral atoms stream bombard the electrodes. It leads to the additional current onto electrodes.

The values of obtained currents and power are given in Table3. The energy dependence of cross sections of the processes for nitrogen was taken from [12]. During defining the ion positive ions current generated by the ionization of target gas flowing out, the potential drop through the hole in high voltage electrode was taken into account.

Table 3. Values of secondary currents of electrons I_e, positive ions I_i, atoms I₀ and the corresponding power at the acceleration of 40 mA beam at a gas pressure 10^–6 Torr. The length of the each accelerating tractunder consideration was equal to 370 mm.

For 10^-6 Torr pressure in accelerating gap the additional currents onto the intermediate electrodes does not exceed 10 m A and does not cause the substantial change in potential distribution on the electrodes. For the worse vacuum the determining of currents onto the electrodes requires more detailed investigation, although it's obvious that parasitic electrons and atoms pass their energy mainly to high voltage electrode, but parasitic positive ions – to ground electrode.

Owing to possible potential drop in the beam in accelerating tract and overcompensation of beam space charge in the stripper [26] the positive ions of residual gas generated in space between the stripping tube and hole in high voltage electrode will be drifted effectively to the accelerating gap and then accelerated. To suppress this undesirable effect (kilowatts of power for the full acceleration of all ions) it's necessary to deflect inside high voltage electrode these secondary low energy charged particles from the axis of the main beam.

The dissociation of target gas molecules by ion beam

There are small amount of hard data about dissociation cross-sections. It's known [12, 27], that these cross-sections are in approximate correspondence to the ionization cross-sections, therefore let us consider s _d = 1,5 ? 10^–16 cm² [29]. The dissociation is produced by both 1 MeV ion and generated 500 eV electrons. As an upper approximation it's possible to consider the electron current twice as large as beam current I. So the flux of dissociation products is I_d = 3 I n l s _d ~ 15 I = 0,6 equiv. Amps. It is comparable with gas flux from the stripping tube. Since the energy of dissociated nitrogen atoms is of the order of several eV [28], then to obtain the desirable thickness of stripper the gas flow should be much more than estimated by conductance. For several gases such as carbon dioxide the flux of dissociation products equal to 150 mTorr l/s, can not be pumped by cryogenic pumps. This effect affects on the choice of "cryogenic" gas.

Thermal processes

The experimental testing of the effects considered above and solutions used in design of 2.5 MeV tandem-accelerator will be carried out on the small accelerator-prototype produced before [ 1] . The target and cryogenic pump of the prototype are shown in Fig. 7.

Estimation of the stripping tube and gas volume temperature

The stripping tube is mounted on the shell of gas volume, the temperature of which is determined by radiation heat fluxes between shell and nitrogen trap, between "ground" electrode and outer frame through the heat shield (it's role plays the high voltage electrode) and by heat penetration from the environment through ceramic insulator.

Forced cooling of the stripping tube

In order to increase the heat removal, the outer diameter of copper stripping pipe 250 mm in length is increased to 16,5 mm. All the tube excepting its center is winded by copper cooling pipe with good heat contact between them. The outer diameter of cooling pipe is 6 mm, the inner 5 mm. For the oil velocity 4 m/s and the heat emission coefficient a = 2000 W m^–2 K^–1 [32] the average temperature difference between the stripping tube wall and oil will be 36° C [30, 31]. The wall temperature of the stripping tube will be 80 ° C, it will allow to use transformer oil without its special refinement from water. The pressure drop on supplying polyethylene tube of 4 m length and 1 cm in diameter is 0,1 bar., it much less than the pressure drop 3 bar. on the cooling pipe for 4 m/s oil velocity. It's known that pressure drop of 3 bar does not lead to the destruction of polyethylene tube with heat carrier.

So, the 5 kW power removal from the high voltage electrode can be obtained. The further increase of heat removal requires the rise of oil velocity in the system, which results in almost square (by velocity) pressure rise.

It has been defined that gas stripping target, used for stripping of H^– ions accelerated to half of total energy, is the most preferable for the electrostatic tandem-accelerator with vacuum insulation on energy of protons up to 2,5 MeV and with dc current up to 40 mA. Three variants of gas stripping target were chosen for further development and realization:

1. Argon gas target with external pumping. This target is attractive by the lack of dissociation effects, but requires to provide beam passage less than 10 mm in diameter on 400 mm length.

2. Argon gas target with turbo-molecular pump in immediate vicinity and with recirculation. It allows to weaken requirements on beam transportation and improve gas conditions.

3. Target with cryogenic nitrogen pump in immediate vicinity. It also allows to weaken requirements on beam transportation, but its use is accompanied by many effects which require experimental testing.

The final choice of the stripping target variant will be done after prepared experiments on the prototype of accelerator tandem.

References