The dynamics of a high-current proton beam in the cusp magnetic field and in the uniform magnetic field of the drift region in the presence of an accelerating field in the cusp region and of two types of compensating electron beams (before and after the cusp) has been studied. It is shown that for the taken beam parameters and magnetic field it is impossible to accelerate a proton beam of the density higher than 10¹² cm⁻³ with maintaining its initial transverse size and monoenergeticity.Вивчено динаміку сильнострумового протонного пучка в магнітному полі каспа та в однорідному магнітному полі дрейфової області за наявності в області каспа прискорюючого поля та двох типів електронних пучків (до і після каспа). Для вибраних параметрів пучків та магнітного поля показана неможливість прискорити протонний пучок щільністю понад 10¹² см⁻³  зі збереженням його поперечних розмірів та моноенергетичності.Изучена динамика сильноточного протонного пучка в магнитном поле каспа и в однородном магнитном поле дрейфовой области при наличии в области каспа ускоряющего поля и двух типов компенсирующих электронных пучков (до и после каспа). Для выбранных параметров пучков и магнитного поля показана невозможность ускорить протонный пучок плотностью большей 10¹² см⁻³  с сохранением его поперечных размеров и моноэнергетичности

Fedorovskaya, O.V.

Maslov, V.I.

Onishchenko, I.N.

Наукова електронна бібліотека періодичних видань НАН України (Vernadsky National Library of Ukraine)

ISSN 1562-6016. ВАНТ. 2022. №3(139)                 109 https://doi.org/10.46813/2022-139-109 ACCELERATION OF A HIGH-CURRENT PROTON BEAM  IN A LINEAR INDUCTION ACCELERATOR  AT ITS COMPENSATION BY ELECTRON BEAMS O.V. Fedorovskaya, V.I. Maslov, I.N. Onishchenko National Science Center “Kharkov Institute of Physics and Technology”, Kharkiv, Ukraine E-mail: onish@kipt.kharkov.ua The dynamics of a high-current proton beam in the cusp magnetic field and in the uniform magnetic field of the drift region in the presence of an accelerating field in the cusp region and of two types of compensating electron beams (before and after the cusp) has been studied. It is shown that for the taken beam parameters and magnetic field it is impossible to accelerate a proton beam of the density higher than 1012 cm-3 with maintaining its initial transverse size and monoenergeticity.  PACS: 41.75.-i, 52.40.Mj, 52.58.Hm, 52.59.-f, 52.65.Rr  INTRODUCTION The production and acceleration of high-current ion beams is the problem of current interest in several im-portant applications: controlled thermonuclear fusion with magnetic confinement, inertial thermonuclear fu-sion on heavy-ion beams of a linear induction accelera-tor (LIA), surface modification of various materials, radiation materials science, etc. In [1 - 4], numerical simulation using the 2.5D code “KARAT” [5], devoted to charge and current compen-sation by electron beams of high-density ion beams of an initial energy 36 MeV in the accelerating gap located in the middle part of the cusp magnetic system, was carried out. It is shown that during the acceleration of such ion beam, the compensation by electron beams ensures the preservation of the ion beam transverse di-mensions and monoenergeticity. The similar investigation [6], performed for the in-jection of high-density ion beams with a lower energy of several hundred kiloelectronvolt, which is typical for existing high-current ion sources (for example, [7]), in the absence of an accelerating field, showed that a threshold arises in beam density 1012 cm-3, above which transportation is not possible. In this paper, the case of [6] is studied but in the presence of an accelerating field in the cusp region. The dynamics of a proton beam in the magnetic field of a cusp configuration and in the uniform magnetic field of the drift region with compensation by the axial electron beam, injected into the first half of the cusp, and by the electron beam, injected along the radius into the second half of the cusp, is studied depending on the beam den-sity.  The dynamics of the proton beam is considered for the cases of the high (3.4 T) and low (0.34 T) magnetic fields in order to determine the degree of magnetic iso-lation of electrons before the acceleration of the proton beam and its compensation after it left the accelerating gap. 1. PROBLEM FORMULATION The studies were carried out using 2.5-dimensional numerical simulation in rz-geometry (Fig. 1). In consid-ering model, the computational region consists of accel-erating and drift parts. The magnetic field is created by two coils with opposite currents (to create so called “casp”) and a solenoid (to create drift region of the uni-form magnetic field). It is followed by another cusp in the case of a multisectional induction accelerator. Two values of magnetic field are taken B0 = 3.4 and 0.34 T. The length of the system zL = 50 cm, radius  rL = 7 cm. From the left, tubular proton beam (energy Wi = 240 keV) and the main electron beam (energy Wе = 130 eV) of the same speed (vi = vе) and density (ni = nе), with inner and outer radii rmin = 0.7 cm, rmax = 1.4 cm are injected. Another electron beam (addi-tional one) is radially injected from the periphery uni-formly over the azimuth toward the axis into the second half of the cusp. The parameters of this electron beam and the value and the topography of the magnetic field of the cusp are chosen so that transverse sizes and densi-ties of electron and proton beams are coincided in drift region. Three values of the proton beam density ni =1010, 1011, 1012 cm-3 are considered. Electric field in the accelerating gap of the length of 1 cm Ez= 240 kV/cm is applied before the middle of the cusp. The distance between the coils is 3 cm.  Fig. 1. The magnetic system geometry and the regions of injection of a proton and two electron beams 2. DYNAMICS OF THE PROTON BEAM  OF VARIOUS DENSITIES IN THE PRESENCE OF ACCELERATING FIELD 2.1. HIGH MAGNETIC FIELD The case of the accelerating gap electric field pres-ence in the absence of the additional electron beam. The results obtained in a high magnetic field are given for a time instant of 70 ns, when the stationary regime has already achieved. For the density of the proton and electron beams ni = ne = 1011 cm-3, as it can be seen from Fig. 2,a, in the 110              ISSN 1562-6016. ВАНТ. 2022. №3(139) absence of an accelerating field the electron beam moves along the magnetic field lines and drags along the essential part of the ion beam to the periphery. It means that electrons are magnetized enough to follow up the magnetic field lines. As for the njn magnetized proton beam of such density it is influenced more by the polarization field strong enough to change its rectilinear motion. In the presence of an accelerating field (see Fig. 2,b), the electron beam is reflected from the accel-erating gap, and the ion beam gets into the accelerating gap and is accelerated and passes through the cusp. But similarly to simple transportation of the ion beam (see Fig. 2,a and [6]) in the drift region it “inflates” due to its drift in crossed electric and magnetic fields that looks like beam corrugation. So the accelerating field does not allow avoiding the increase of ion beam transverse size. For the density of the proton and electron beams ni = ne = 1012 cm-3 (see Fig. 2,c,d) electron beam drags along almost the whole ion beam to the periphery with or without accelerating field. The case of the presence both the accelerating gap electric field and the additional electron beam. At the density of the proton beam ni = 1010 cm-3, as well as in the accelerating field absence in a strong magnetic field [6], the following particle dynamics aris-es. In the radial electric field of space charge and polari-zation field and the longitudinal external magnetic field the complicated motion of protons occurs. Resulting azimuthal drift of the proton beam is observed as its periodic corrugation along the drift region (Fig. 3,a). Energy gain of the proton beam is corresponded to the accelerating field (total proton beam energy after the cusp Wi = 480 keV), that retains along the drift region (see Fig. 3,b).  The main electron beam does not reach the cusp un-der the influence of the electric field in accelerating gap and the space charge field of the additional electron beam. This occurs both at low (ni = 1010cm-3) and high (ni = 1012 cm-3) proton beam densities.  Fig. 2. Arrangement of particles of the proton (red) beam and main electron (green) beam, in the absence of an additional electron beam, on the rz-plane:  (a, c) accelerating field is absent; (b, d) accelerating field is applied;  (a, b) ‒ ni = 1011 сm-3; (c, d) ‒ ni = 1012 сm-3  The proton beam with density ni = 1011 сm-3 diverges in the cusp more strongly, since space charge fields are greater. In the drift region the periodic corrugation of the proton beam occurs (see Fig. 3,c) with amplitude greater than at the density ni = 1010 cm-3. Beside for den-sity ni = 1011 сm-3, the proton beam is accelerated not only by the electric field in the accelerating gap, but also by the increased space charge field of the additional electron beam after cusp (see Fig. 3,d). The decrease in the velocity of the additional electron beam along the magnetic field line at the end of the cusp occurs due to the rearrangement of the radial motion of electrons into a longitudinal one, and therefore the density of the addi-tional beam in this place becomes higher. Behind the region of increased space charge of the additional elec-tron beam, the latter is accelerated, and the proton beam slows down, finally having energy Wi = 480 keV at the system exit. ISSN 1562-6016. ВАНТ. 2022. №3(139)                 111  Fig. 3. Arrangement of particles of the proton (red) beam, main electron (green),  and additional electron (blue) beams, on rz-plane (a, c, e).  Kinetic energy of particles of the proton beam, main electron and additional electron beams vs the longitu dinal coordinate z (b, d, f).  (a, b) ‒ ni= 1010 сm-3; (c, d) ‒ ni = 1011 сm-3; (e, f) ‒ ni = 1012 сm-3  At proton beam density ni = 1012сm-3, its corrugation amplitude is greater (see Fig. 3,f) than in the first two cases, that leads to an increase in its energy spread. The additional electron beam in the end of the cusp is signif-icantly slowed down to 0.5 MeV, and the proton beam acquires energy of 2 MeV due to the space charge of the additional beam and 0.24 MeV in the accelerating elec-tric field (see Fig. 3,f). Further in the drift gap, the pro-ton beam slows down, while the additional electron beam accelerates. At the system exit, the energy of the proton beam is about 2 MeV, since the proton beam accelerated due to two factors: the electric field in the cusp and the space charge field of additional electron beam.  However, as in the absence of an accelerating field [6], both compensating electron beams do not allow maintaining the transverse dimensions of the proton beam after acceleration in the cusp and transport in the drift region to the next section. 2.2. LOW MAGNETIC FIELD Since the magnetic field magnitude changes the par-ticle dynamics, in this subsection options for accelerat-ing a proton beam with densities ni = 1010 сm-3 and ni = 1012 сm-3 are considered for low magnetic fields, the influence on particles of which is not so significant as for B0 = 3.4 T. In contrast to the case when there is no accelerating field, and the magnetic field is B0 = 3.4 T [5], in a the main electron beam, a high-current proton beam (ni = 1012 cm-3) is not dragged along the magnetic field lines by the main electron beam to the periphery, and passes into the drift region together with the electron beam (see Fig. 4,a-d), despite the electric field, deceler-ating the electrons (Fig. 4,a). In this case, the electrons of the main beam, reaching the cusp, lag behind the ions and slightly diverge in the radial direction. As a result, a polarization field arises between the ions and lagging 112              ISSN 1562-6016. ВАНТ. 2022. №3(139) electrons. When the longitudinal component Ez of this field reaches the threshold value, the proton beam drags the electron beam due to the polarization field  (see Fig. 4,a-c). The electrons of the main electron beam (green) are accelerated and pass through the cusp, while the protons (red) are decelerated (see Fig. 4,d). In this case, drift in crossed radial electric and longitudinal magnetic fields is observed in the form of corrugation (see Fig. 4,b-c).     Fig. 4. Arrangement of the particles of the proton (red), main electron (green) beams on the rz-plane at a time of: 20 ns, ni = 1012 сm-3 (a); 60 ns, ni = 1012 сm-3 (b); 120 ns, ni = 1012 сm-3 (c); kinetic energy of the particles  of the proton and main electron beams vs  the longitudinal coordinate z, ni = 1012 сm-3 (d) At a magnetic field B0 = 0.34 T and the presence of both compensating electron beams in the case of ni = 1010 cm-3, the proton beam dynamics is changed: the corrugation amplitude decreased, and its period in-creased (Fig. 5,a).   Fig. 5. Arrangement of the particles of the proton (red), main electron (green) and the additional electron (blue) beams on the rz-plane. ni=1010 сm-3 (а); ni=1011 сm-3 (b) A proton beam with density ni = 1011 сm-3 in a low magnetic field has a larger corrugation amplitude (see Fig. 5,b) than in a high magnetic field (see Fig. 3,c).    Fig. 6. Kinetic energy of the proton (red), main electron (green) and additional electron (blue) beams vs the lon-gitudinal coordinate z. ni=1010 сm-3 (а); ni=1011 сm-3 (b)  b a c d a b b a ISSN 1562-6016. ВАНТ. 2022. №3(139)                 113 Wherein, a proton beam with a density ni = 1010 сm-3 is accelerated in the electric field, having energy about 500 keV at the cusp exit (Fig. 6,a). The proton beam with a density of ni = 1011 сm-3 is accelerated due to both the electric field and the space charge field of the additional electron beam (Wadd = 0.5 MeV), which made it possible to obtain its energy of about 600 keV at the system exit (see Fig. 6,b). At density of 1012 сm-3, the proton beam “scatters” in the drift region (therefore is not presented), because it is not compensated by a radially injected electron beam. The proton and electron beams have been moved apart in space – the electron beam moves along the magnetic field lines, and the proton beam “sweepingly” drifts in crossed radial electric and external longitudinal magnetic fields, reaching the walls of the chamber. Thus, in the consid-ered case of a weak magnetic field, there exists a densi-ty threshold, when compensation becomes impossible. CONCLUSIONS Dynamics of a high-current proton beam in a mag-netic cusp with an accelerating gap and in an uniform magnetic field of drift region, using charge and current compensation before entering the accelerating gap by an axial electron beam, injected into the first half of the cusp, and after leaving the accelerating gap by an elec-tron beam, injected along radius to the second half of the cusp, was studied depending on the density of the proton and electron beams. Such a scheme is of interest as an injector, in particular, in the problem of heavy-ion inertial fusion using a high-current ion beam of LIA. The results of numerical simulation show that for all considered beam densities (1010…1012cm-3) corrugation of the tubular proton beam occurs in the drift region, caused by proton drift in the crossed longitudinal exter-nal magnetic field and the radial electric field of un-compensated beams. This leads to an increase in trans-verse dimensions and energy spread, in contrast to the results of [1-4], and to the similar dynamics for simple proton beam transport without acceleration [6]. The threshold density of the proton beam, for which it be-comes unsuitable for injection into the subsequent ac-celerating section, remains the same 1012 cm-3, as in [6]. In a low magnetic field the dynamics of deteriora-tion in the quality of the proton beam in the scheme under consideration is more obvious and there is the density threshold too. This is due to the weakening of the magnetic isolation of electrons at lower magnetic fields. For the same reason, in a lower magnetic field, two phenomena that are not foreseen by the idea under study of compensation by two electron beams arise. First, the axial beam is dragged by the proton beam into the accelerating gap. Secondly, the proton beam, in ad-dition to acceleration in an external electric field, expe-riences additional acceleration in the space charge field of the additional radially injected electron beam. The results, obtained in this paper, force us to recon-sider the original concept of ion beam compensation by electron beams or to limit ourselves to an ion beam den-sity lower than 1012 cm-3. REFERENCES 1. V.I. Karas’, E.A. Kornilov, O.V. Manuilenko, O.V. Fedorovskaya. Рarticle dynamics in the injector of ion linear induction accelerator // Problems of Atomic Science and Technology. Series “Nuclear Physics Investigations”. 2019, № 6, р. 85-89. 2. V.I. Karas’, E.A. Kornilov, O.V. Manuilenko, O.V. Fedorovskaya. Рarticle dynamics in the injector of ion linear induction accelerator // Problems of Atomic Science and Technology. Series “Plasma Electronics and New Methods of Acceleration”. 2008, № 4, р. 83-88. 3. V.I. Karas’, N.G. Belova. Acceleration and stability of high-current ion beams in two accelerating gaps of a linear induction accelerator // Plasma Phys. Rep. 1997, v. 23, № 4, p. 328-331.  4. V.I. Karas’, O.V. Manuilenko, E.A. Kornilov, V.P. Tarakanov, O.V. Fedorovskaya. Dynamics of high-current ion beam in the drift gap of induction accelerator at different variants of charge compensa-tion // Problems of Atomic Science and Technology. Series “Plasma Physics”. 2014, № 6, p. 104-107.  5. V.P. Tarakаnov. User’s Manual for Code KARAT // Springfield VA: Berkley Research Associates Inc. 1992, p. 137.  6. I.N. Onishchenko, O.V. Fedorovskaya. Simulation of the compensation of a high-current ion beam by an electron beam in a cusp magnetic system // Prob-lems of Atomic Science and Technology. Series “Plasma Electronics and New Methods of Accelera-tion”. 2021, № 4, p. 122-127. 7. Hiroaki Ito, Yasushi Ochiai and Katsumi Masugata. Development of High-current Pulsed Heavy-ion-beam Technology for Applications to Materials Pro-cessing // Journal of the Korean Physical Society. 2011, v. 59, № 6, p. 3652-3656. Article received 12.06.2022  ПРИСКОРЕННЯ СИЛЬНОСТРУМОВОГО ПРОТОННОГО ПУЧКА В ЛІНІЙНОМУ ІНДУКЦІЙНОМУ ПРИСКОРЮВАЧІ ПРИ ЙОГО КОМПЕНСАЦІЇ ЕЛЕКТРОННИМИ ПУЧКАМИ О.В. Федоровська, В.I. Маслов, I.М. Оніщенко Вивчено динаміку сильнострумового протонного пучка в магнітному полі каспа та в однорідному магнітному полі дрейфової області за наявності в області каспа прискорюючого поля та двох типів електронних пучків (до і після каспа). Для вибраних параметрів пучків та магнітного поля показана неможливість прискорити протонний пучок щільністю понад 1012 см-3 зі збереженням його поперечних розмірів та моноенергетичності. УСКОРЕНИЕ СИЛЬНОТОЧНОГО ПРОТОННОГО ПУЧКА В ЛИНЕЙНОМ ИНДУКЦИОННОМ УСКОРИТЕЛЕ ПРИ ЕГО КОМПЕНСАЦИИ ЭЛЕКТРОННЫМИ ПУЧКАМИ О.В. Федоровская, В.И. Маслов, И.Н. Онищенко Изучена динамика сильноточного протонного пучка в магнитном поле каспа и в однородном магнитном поле дрей-фовой области при наличии в области каспа ускоряющего поля и двух типов компенсирующих электронных пучков (до и после каспа). Для выбранных параметров пучков и магнитного поля показана невозможность ускорить протонный пучок плотностью большей 1012 см-3 с сохранением его поперечных размеров и моноэнергетичности. 

Acceleration of a high-current proton beam in a linear induction accelerator at its compensation by electron beams

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Acceleration of a high-current proton beam in a linear induction accelerator at its compensation by electron beams

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