The laser acceleration of plasmoids is investigated theoretically. Preliminary studies suggest that this configuration, which is based on the forced oscillations of finite pieces of plasma contained in moving or vibrating r.f. wells, has very much simplified plasma physics compared to that of other plasma-based ion acceleration schemes. It is necessary to consider the case when the applied electric field, E, of frequency {omega}, is large, E {le} e/4{pi}{var_epsilon}{sub o}r{lambda}, where r is the Classical electron radius and when the plasma density, n, is high n < 1/r{lambda}{sup 2}. Realization of this proposal requires the development, among other things, of biresonant accelerating systems including oversized single-mode tue-like resonators and the connection of this resonator to a terawatt FELs. If these problems, which will be delineated, are overcome--and progress in optics gives one reason to believe they can be--then gradients of {approximately} 10 GeV/m can be attained. Preliminary design of a linac, based upon this proposal and of a proof-of-principle experiment are presented

Dzergach, A. I.

Kabanov, V. S.

Sessler, A. M.

Wurtele, J. S.

UNT Digital Library

N L- 4 1966 ERNEST ORLANDO LAWRENCE BERKELEY NATIONAL ABORATORY ""-w About the Realization of Laser Acceleration Schemes Based on Plasmoids in R.F. Wells s@ u g lgg8 0 s 7 I A:M. Sessler, J.S. Wurtele, A.I. Dzergach, and V.S. Kabanov Accelerator and Fusion Research Division June 1998 Presented at the DISCLAIMER This document was prepared as an account 'of work sponsored by t h e  United States Government. While this document is believed to contain correct information, neither the United States Government nor a n y  agency thereof, nor The Regents of the University of California, nor a n y  of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of  any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or The Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of t h e  United States Government or any agency thereof, or The Regents of the University of California. Ernest Orlando Lawrence Berkeley National Laboratory is an equal opportunity employer. DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. I LBNL-4 1966 CBP Note-248 About the Realization of Laser Acceleration Schemes Based on Plasmoids in R.F. Wells* A. M. Sessler, J. S. Wurtele Lawrence Berkeley National Laboratory University of California, Berkeley, California 94720 A. I. Dzergach, V. S. Kabanov Moscow Radiotechnical Institute Moscow, Russia 113 519 June 1998 presented at the European Particle Accelerator Conference Stockholm, Sweden June 22-26,1998 I * This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, High Energy Physics Division, of the U. S. Department of Energy, under Contract No. DE-AC03-76SF00098. I ABOUT THE REALIZATION OF LASER ACCELERATION SCHEMES BASED ON PLASMOIDS IN R.F. WELLS A.I. Dzergach, V.S. Kabanov, MRTI, 113 519, Moscow RUSSIA A.M. Sessler, J.S. Wurtele, LBNL, Berkeley, CA 94720 USA Abstract The laser acceleration of plasmoids [ 11 is investigated theoretically. Preliminary studies suggest that this configuration, which is based on the forced oscillations of finite pieces of plasma contained in moving or vibrating r.f. wells, has very much simplified plasma physics compared to that of other plasma-based ion acceleration schemes. It is necessary to consider the case when the applied electric field, E, of frequency w, is large, E S e/47EEdh, where r is the Classical electron radius and when the plasma density, n, is high n<l/rh2. Realization of this proposal requires the development, amongst other things, of biresonant accelerating systems including oversized single-mode tube-like resonators and the connection of this resonator to a terawatt FELs. If these problems, which will be delineated, are overcome--and progress in optics gives one reason to believe they can be then gradients of -10 GeVIm can be attained. Preliminary design of a linac, based upon this proposal and of a proof- of-principle experiment are presented. 1 INTRODUCTION Accelerator based on plasmoids in wells (APW) schemes may be treated as an intermediate variant between collective accelerators [ 1,2] and classical linacs. Strong concentrated e.m. waves [3] create r.f. wells [4,5] which localize the plasmoids. The r.f. wells may be dee (-keVs), if the e.m. field amplitude is Em= mc2/eA., mc , e being the electrons rest energy and charge, A the field wavelength [6, 71. Three schemes of acceleration are possible: moving well accelerator, (MWA), plasmoids grating accelerator (PGA) and moving plasmoids grating accelerator, Having in mind the necessity of detailed analytical and numerical studies of basic processes in the conceptual accelerators we consider here (after a short review of preliminary results) some aspects of realization of the MWA and the PGA scheme. The MWA is a collective accelerator and, as such, can accelerate of all atomic numbers and, consequently, is of general interest. The PGA is subject to the same guiding and energy transfer restrictions of any plasma accelerator. That is, without some form of guiding the efficiency (beam energy I laser energy) is very low. The subject of guiding is not addressed in this paper, but would, of course, have to be addressed in future work. We can envision at least two possible ways in which guiding can be achieved. The first is to form a number of lines of plasmoids so as to make a “dielectric tube” around the accelerated beam and thus to guide the accelerating laser P beam. The second method, is to have the accelerator within an overmoded tube and to have “tube guiding”. The overmoding must be sufficient so as to reduce the surface field to a manageable intensity. So, in the rest of this paper we address the basic physics of the PGA, but realize that we are defemng a vital element to the future. An approximate description of the e.m. fields is given by cylindrical waves E,,, (q,r,z) = TMom in an oversized tube (Fig. 1). Ez=EmJo (R) sin2 sincot, etc., R = k,r, z=k,z. I I I  Fig. 1 R.F. wells in the field Eomn. The r.f. wells localize spheroidal (s) or toroidal ( t )  plasmoids near the nodes of the e.m. field (Fig. 1). Linearized equations of rz-motion near a center of a well (r = Z = 0) are: y “ ( ~ ) + ( a , , + 2 q , , ~  sin2x)y=0, (2) where y=r or z,  2x=wt, qz = -24, = eEm h ~ o s  o b /  mc2,  8, =arctg (kr / k,) = the BriIlouin angle; ar,Z are proportional to the Coulomb gradient. Azimuthal symmetry gives an integral mr’ (dq I dt) = const. The curves r (t)  and z (t)  are similar to betatron oscillations in AG systems. These results are supplemented by [8]. The condition of strong AG focussing in an r.f. well qz = 0.5, (3) is similar to the wave-breaking limit [1,2]. A limit for plasma density in r.f. wells for small fields, q2 <<I, is n < m d ~ , / 2 e ~  [4,5]. This value was confirmed for strong fields, q2 = 0.5 by numerical simulation [6b]. These results suggest the possibility of accelerating field E, (gradient of ponderomotive potential).E, = 0.1 E,,,. The ratio of the axial and surface cylindrical fields is Equations (3) and (4) define the tube radius: (4) R ~ ~ L  = (qzmc ’/ e ~ ,  )’ / (COS ’ e, sin e, ). (5) One may see that minimal demands are required of the plasma, namely, stability of small (several Debye lengths) plasrnoids in r.f. wells. 2 SCHEMES OF THE MOVING WELLS ACCELERATOR(MWA)AND PLASMOIDS GRATING ACCELERATOR (PGA) A schematic of a MWA (Fig. 2) consists of an oversized (e.g. axially symmetric) converging waveguide 1 with diffraction gratings (azimuthal grooves) at the ends. Two counter propagating waves (@la, u2,,) are excited by lasers 1A and 2A. The z- velocity of r.f. wells (plasmoids) V(z)= (ol - a,) / [k,(z)-k,(z)] may be increased by a factor of 2-3 in each section. Each section must have larger difference of frequencies 0, - w, , than the preceding one. Possible values of basic parameters are A,,* - 20 pm, R, - 5mm, L,-lOcm, accelerating gradient SGVfm; laser energy We,- lOJ/section. Positive ions may be accelerated from p,- 0.001 to p,- 0.3 in - 6 sections. SeccionA S d o n B  U ~ I A  - ~ I B  PIB -”LB Fig 2. Schematic of a MWA Section. lALK”I I ! - I - ! I INA l  I I L’f ! I I -,- In A 1 / 1 1  I --!-- I II\ I I I Fig. 3 Schematic of a PGA section. A schematic of a section of the PGA (Fig. 3) is similar to an axially symmetric version of the usual ring optical open resonator but with plasmoids and accelerated bunches along its z-axis. It consists of 3 coaxial tubes 1,2,3, two coaxial cut cones (or washers) 4 and two ring-like Fabri- Perot etaions 5. Another possible variant is beads of plasma forming a grating are formed mechanically, without a forming field. Single-mode for both frequencies is ensured, as in usual single-mode lasers, by diffraction gratings (azimuthal grooves) at the ends of the tube 1 and cones 4, and by the Fabri-Perot etalons 5. Crossed action of the grooves (2-dimensional filtering) is possible, if the number of half-zigzags in the tube 1 is odd. The grating of plasmoids is formed and fixed by the forming field E fo,,,,,, and then a slow wave is excited along it by the exciting wave E eom, whose frequency is somewhat lower, WJ of =p,(e/n) cos e, , (6) fib being the accelerated beam (bunches) velocity, 8 = phase advance of the slow wave per cell of the grating, 8 bf =the Brillouin angle of forming field. E.g. if Bb=I, 8=n/2, cos e,,=O.9, then @,/of =.0.45. The focussing of positive pmcles accelerated in the PGA may be ensured by some excess of electrons in the plasmoids. In case of acceleration of electrons the defocussing by the slow accelerating wave is much less [7] than the AG focussing by the forming field. The e.m. field energy per unit length of the tube 1 is w, / L =  112 E, E , Z ~  R,Z , (7 1 An experimental section may have the diameter 2Rs = lcm, length L,= 6cm, and the field energy -10 J (h=20pm). Some parameters of 3 variants of experimental PGA sections (wavelength, tube radius R, and length L,, field amplitude E,, accelerating field E,, accelerated particles energy L,Ea, e.m. field energy in the tube Wem) are given in the Table 1 for the E,= 1 GV/m: Table 1: Three variants of experimental PGA sections. R, Ls E m  Ea L A  We, pm cm crn GV/m GV/m MeV J 20 0.5 6 50 5 300 6 30 0.3 4 30 3 120 2 100 0.1 1.2 10 1 22 0.05 -1 -1 -1 -1 -2 -3 The last line of the table gives the degree of dependence of the above parameters on the wavelength h. The accelerated particles may be positive ions, electrons and positrons. The first variant seems to be preferable. Comparison of beam currents in the PGA and usual linacs is based on an assumption that the number of accelerated particles per bunch is -0.1 of the number of electrons in a plasmoid (- 0.01 h/r ) and the number of bunches per unit length is -22,- e ;  it shows that both currents may be - equal in case of spheroidal plasmoids (in the case of toroidal wells larger values are possible). l e ’  3 A MODEL FOR A PROOF-OF- PRINCIPLE EXPERIMENT This model (Fig. 4) is based on an existing Nd-glass plane polarized laser with a wavelength he- Ipm, pulse energy - lJ, and pulse length cz - lmm and power 300 GW. A periodical dielectric structure (“beads”) replaces the plasmoid grating fixed by the forming field. The density of these “beads” must be about 0.3~=3x1Orncrn -3. 2 5 ACKNOWLEDGEMENTS This work was partially supported by the U.S. Department of Energy, Office of Energy Research, Office of High Energy and Nuclear Physics, under Contract No. DEA-AC03-76SF0098. The authors are thankful to M. Zolotorev for helpful discussions. One of the authors (A.I.D.) is thankful to LBNL and to the International Science and Technology Center for support of this work. Fig. 4 Scheme of proof-ofiprinciple experiment. The period of this structure should be in accordance with usual linac rule (6) &/ 2 =0.2pm. Only one wavelength k h ,  is used in this case: inertia of the plasma ions gives the possibility to use this grating during a short time - 3 psec. The model consists of a beam splitter, 2 mirrors, 2 prisms and 2 lenses, which give a pair of intersecting beams. The dielectric grating (“beads” with a period 4 5 )  is placed at the point of beams crossing. The focal length of the lenses is -lm, the light beams width at the region of crossing is -1mm. The amplitude parameter must be qz = 0.4, in order to have strong AG focussing. It gives the amplitude of field E,=lTV/m in the focal (crossing) region. Plane polarization of the laser field leads to one dimensional focussing instead of %-dimensional, in the case of a cylindrical field, so we expect some defocussing in the 2nd direction; the principal effect will be present. Two- dimensional focussing may be realized by means of a second set of elements, as shown in Fig 4, but disposed in the orthogonal plane (y instead of x). The ex ected value of accelerating gradient is E,=lOO kVA=lO V/m, which corresponds to an energy gah in the focal region (-lmm) 1OOMeV. R 4 CONCLUSIONS Preliminary analytical and numerical studies of charged particles motion in the cylindrical field TM,,, (cp,r,z) show the existence of deep (-keVs) 3-dimensional r.f. wells (h.f. traps), steady or moving, for electrons (positrons) at field densities - lMV/L. Preliminary numerical studies of plasmoid dynamics confirm the above data up to the plasma densities -50% of the critical (o=w& value. Various schemes for the acceleration of positive ions, electrons and positrons by means of plasmoids, captured in r.f. wells, are discussed. Expected values of accelerating gradient are -100 keVA Two variants of experimental models are proposed: a section of accelerating structure (plasmoids grating in a tube with a diameter -1cm and length -6cm, e.m. field energy - 65 wavelengths k 2 0  and 40 pm, energy gain 300 MV, and a proof-of-principle experiment (dielectric “beads” grating, Nd-glass laser, energy - 1 J, pulse length cz- lmm, energy gain -100 MV). 6 REFERENCES [ 13 A.M. Sessler, “ Collective-Field Acceleration”, €’roc. VII-th Int. Particle Accelerators Conf., Yerevan, 1969, 2, 43 1 (1970). [2] E. Esarey, et at. IEEE Trans on Plasma Sci., 14, N0.2,252-288 (1996). [3] K. Shimoda, Applied Optics, 1 ,3  (1962). [4] H. Motz and C.J. H. Watson, “ The radio-frequency confinement and acceleration of plasmas”, Advances in Electronics, ed. by L. Marton, Acad. Press, New -York, N.Y. 153 (1967). [SI I.R. Gekker, “ The Interaction of strong electromagnetic waves with plasmas”, Clarendon Press, Oxford, 1982 (transl. from Russ.). [6a] A.I. Dzergach, Proc 4th European Particle Accelerator Conference, EPAC-94, Vol. 1,8 14-816. [6b] A.I. Dzergach, V.S. Kabanov et al, ibid., 811-813. [7] A.I. Dzergach, Europhys. Let. 2 9 (7) 525-530 (1995). [8] J.M. Finn. et al., “ Physics of Plasmas” 4 (3, 1238- 1248 (1997). [9] A.M. Sessler, Proc of the Workshop on Laser Acceleration of Particles, 1982, AIP Conf. Proc. 91, 154 (1982). [lo] A.M. Sessler, E. Sternbach and J.S. Wurtele, Nucl Instrum. and Methods in Phys. Res. B-40/41, 1064-1068 (1989). [ll] K-J Kim, M Xie and A.M. Sessler, Nucl. Instr. a Method. in Phys. Res. A375 No. 1-3 (17th Int. FEL Conf). 523-525 (1996). [12] P. Morton and S. Chattopadhyay, Nucl. Instr. and Meth. in Phys. Res. A358, No. 1-3 (16th Int. FEL Conf) E131 N.S. Ginzburg et al, IEEE Trans. on Plasma Sci. [14] R.D. Boyd et al, Applied Optics, 34, No. 10, 1697- 1706 (1995). [15] B.W. Shore et al, J. Opt. SOC. Am. M o l  14, 138-141 (1995). V0124, NO. 3,770-780 (1996). NOS, 1124-1136 (1997). 3 

About the realization of laser acceleration schemes based on plasmoids in r.f. wells

Sessler, A M

Wurtele, J S

Dzergach, A I

Kabanov, V S

eScholarship - University of California

Lawrence Berkeley National LaboratoryLBL PublicationsTitleAbout the Realization of Laser Acceleration Schemes Based on Plasmoids in R.F. WellsPermalinkhttps://escholarship.org/uc/item/2wd0m9csAuthorsSessler, A MWurtele, J SDzergach, A Iet al.Publication Date1998-06-01Copyright InformationThis work is made available under the terms of a Creative Commons Attribution License, available at https://creativecommons.org/licenses/by/4.0/eScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaLBNL-41966 ORLANDO LAWRENCE NATIONAL LABORATORY ERNEST BERKELEY About the Realization of Laser .Acceleration Schemes Based on Plasmoids in R.F. Wells AM. Sessler, J.S. Wurtele, A.I. Dzergach, and V.S. Kabanov Accelerator and Fusion Research Division June 1998 Presented at· the European Particle .. , (') 0 :::c "C (I) I< -tI .... I [Jl 2 I I 01:> t-' I.Cl 01 01 DISCLAIMER This document was prepared as an account of work sponsored by the United States Government. While this document is believed to contain correct information, neither the United States Government nor any agency thereof, nor the Regents of the University of California, nor any of their employees, makes any warranty, express or implied, or assumes any legal responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by its trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or the Regents of the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof or the Regents of the University of California. LBNL-41966 CBP Note-248 About the Realization of Laser Acceleration Schemes Based on Plasmoids in R.F. Wells* A. M. Sessler, J. S. Wurtele Lawrence Berkeley National Laboratory University'of California, Berkeley, California 94720 A. I. Dzergach, V. S. Kabanov Moscow Radiotechnical Institute Moscow, Russia 113 519 June 1998 presented at the European Particle Accelerator Conference Stockholm, Sweden June 22-26, 1998 * 'This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, High Energy Physics Division, of the U. S. Department of Energy, under Contract No. DE-AC03-76SF00098. ABOUT THE REALIZATION OF LASER ACCELERATION SCHEMES BASED ON PLASMOIDS IN R.F. WELLS A.I. Dzergach, V.S. Kabanov, MRTI, 113519, Moscow RUSSIA A.M. Sessler, l.S. Wurtele, LBNL, Berkeley, CA 94720 USA Abstract The laser acceleration of plasmoids [1] is investigated theoretically. Preliminary studies suggest that this configuration, which is based on the forced oscillations of finite pieces of plasma contained in moving or vibrating r.f. wells, has very much simplified plasma physics compared to that of other plasma-based ion acceleration schemes. It is necessary to consider the case when the applied electric field, E, of frequency ro, is large, E :s; e/41tEorA., where r is the Classical electron radius and when the plasma density, n, is high n<1IrA.2• Realization of this proposal requires the development, amongst other things, of biresonant accelerating systems including oversized single-mode tube-like resonators and the connection of this resonator to a terawatt PELs. If these problems, which will be delineated, are overcome--and progress in optics gives one reason to believe they can be-then gradients of -lOGe V 1m can be attained. Preliminary design of a linac, based upon this proposal and of a proof-of-principle experiment are presented. 1 INTRODUCTION Accelerator based on plasmoids in wells (APW) schemes may be treated as an intermediate variant between collective accelerators [1,2] and classicallinacs. Strong concentrated e.m. waves [3] create d. wells [4, 5] which localize the plasmoids. The r.f. wells may be deep (-keVs), if the e.m. field amplitude is Em= mc%)., mc , e being the electrons rest energy and charge, ). the field wavelength [6, 7]. Three schemes of acceleration are possible: moving well accelerator, (MW A), plasmoids grating accelerator (PGA) and moving plasmoids grating accelerator. Having in mind the necessity of detailed analytical and numerical studies of basic processes in the conceptual accelerators we consider here (after a short review of preliminary results) some aspects of realization of the MW A and the PGA scheme. The MW A is a collective accelerator and, as such, can accelerate of all atomic numbers and, consequently, is of general interest. The PGA is subject to the same guiding and energy transfer restrictions of any plasma accelerator. That is, without some form of guiding the efficiency (beam energy I laser energy) is very low. The subject of guiding is not addressed in this paper, but would, of course, have to be addressed in future work. We can envision at least two possible ways in which guiding can be achieved. The first is to form a number of lines of plasmoids so as to make a "dielectric tube" around the accelerated beam and thus to guide the accelerating laser beam. The second method, is to have the accelerator within an overmoded tube and to have "tube guiding". The overmoding must be sufficient so as to reduce the surface field to a manageable intensity. So, in the rest of this paper we address the basic physics of the PGA, but realize that we are deferring a vital element to the future. An approximate description of the e.m. fields is given by cylindrical waves Eomn (cp,r,z) = TMomn in an oversized tube (Fig. 1). Ez=Eml 0 (R) sinZ sinrot, etc., R = krr, z=k,z. - (1) -+ J..j2 -+-Fig. 1 R.F. wells in the field Eomn. The r.f. wells localize spheroidal (s) or toroidal (t) plasmoids near the nodes of the e.m. field (Fig. 1). Linearized equations of rz-motion near a center of a well (r = z = 0) are: y" (x)+(ar,z+2Qr,z sin2x)y=O, (2) where y=r or z, 2x=rot, qz = -2qr= eEm MaS 9 b lwnc2, 9 b =arctg (krl kz ) = the Brillouin angle; ar,z are proportional to the Coulomb gradient. Azimuthal symmetry gives an integral ml (dcp I dt) = canst. The curves r (t) and z (t) are similar to betatron oscillations in AG systems. These results are supplemented by [8]. The condition of strong AG focussing in an r.f. well (3) is similar to the wave-breaking limit [1,2]. A limit for plasma density in r.f. wells for small fields, q. «1, is n<moleol2i [4,5]. This value was confirmed for strong fields, q. = 0.5 by numerical simulation [6b]. These results suggest the possibility of accelerating field E. (gradient of ponderomotive potential).E. = 0.1 Em. The ratio of the axial and surface cylindrical fields is (4) Equations (3) and (4) define the tube radius: One may see that minimal demands are required of the plasma. namely, stability of small (several Debye lengths) plasmoids in r.f. wells. 2 SCHEMES OF THE MOVING WELLS ACCELERATOR(MWA)AND PLASMOIDS GRATING ACCELERATOR (PGA) A schematic of a MW A (Fig. 2) consists of an oversized (e.g. axially symmetric) converging waveguide 1 with diffraction gratings (azimuthal grooves) at the ends. Two counter propagating waves «(j)la. (j)2a) are excited by lasers lA and 2A. The z- velocity of r.f. wells (plasmoids) V(z)= «(j)1 - (j)2) I [k1(z)-k2(z)] may be increased by a factor of 2-3 in each section. Each section must have larger difference of frequencies (j)1 - (j)2' than the preceding one. Possible values of basic parameters are 1.,1.2 - 20 !lm, R. - 5mm, L.-lOcm, accelerating gradient SGV 1m; laser energy Wern -lOJ/section. Positive ions may be accelerated from ~z - 0.001 to ~z - 0.3 in - 6 sections. Section A SectionB '(I)lA _m18 < COlD - o:za Fig 2. Schematic of a MW A Section. Fig. 3 Schematic of a PGA section. A schematic of a section of the PGA (Fig. 3) is similar to an axially symmetric version of the usual ring optical open resonator but with plasmoids and accelerated bunches along its z-axis. It consists of 3 coaxial tubes 1,2,3, two coaxial cut cones (or washers) 4 and two ring-like Fabri-Perot etalons 5. Another possible variant is beads of plasma forming a grating are formed mechanically, without a forming field. Single-mode for both frequencies is ensured. as in usual single-mode lasers, by diffraction gratings (azimuthal grooves) at the ends of the tube 1 and cones 4. and by the Fabri-Perot etalons 5. Crossed action of the grooves (2-dimensional filtering) is possible. if the number of half-zigzags in the tube 1 is odd. 2 The grating of plasmoids is formed and fixed by the forming field E fomn• and then a slow wave is excited along it by the exciting wave E tom' whose frequency is somewhat lower. (6) ~b being the accelerated beam (bunches) velocity. e = phase advance of the slow wave per cell of the grating. e bf =the Brillouin angle of forming field. E.g. if ~b=l, e=1t12, cos e bf =0. 9. then (j)J(j)f = 0.45. The focussing of positive particles accelerated in the PGA may be ensured by some excess of electrons in the plasmoids. In case of acceleration of electrons the defocussing by the slow accelerating wave is much less [7] than the AG focussing by the forming field. The e.m. field energy per unit length of the tube 1 is 2 R 2 Worn I L "" 112 Eo E. 1t • , (7) e.g .• -100 Jim, if A, =20 !J.m, Rs = 5mm, E.=lGV/m. An experimental section may have the diameter 2Rs = 1 cm, length L. = 6cm, and the field energy -10 J (A,=20f.Lm). Some parameters of 3 variants of experimental PGA sections (wavelength, tube radius Rs and length Ls. field amplitude Em' accelerating field Ea. accelerated particles energy Ls Ea, e.m. field energy in the tube Wern) are given in the Table 1 for the Es= 1 GV /m: Table 1: Three variants of eXEerimental PGA sections. A, R. Ls Ern Ea LsEa Wern !lm cm cm GV/m GV/m MeV J 20 0.5 6 50 5 300 6 30 0.3 4 30 3 120 2 100 0.1 1.2 10 1 12 0.05 -1 -1 -1 -1 -2 -3 The last line of the table gives the degree of dependence of the above parameters on the wavelength 1.,. The accelerated particles may be positive ions, electrons and positrons. The first variant seems to be preferable. Comparison of beam currents in the PGA and usual linacs is based on an assumption that the number of accelerated particles per bunch is -0.1 of the number of electrons in a plasmoid (- 0.01 Alre), and the number of bunches per unit length is -2A,"e; it shows that both ,currents may be "" equal in case of spheroidal plasmoids (in the case of toroidal wells larger values are possible). 3 A MODEL FOR A PROOF-OF-PRINCIPLE EXPERIMENT This model (Fig. 4) is based on an existing Nd-glass plane polarized laser with a wavelength A,e- If.Lm, pulse energy - lJ. and pulse length c't - lmm ana power 300 GW. A periodical dielectric structure ("beads") replaces the plasmoid grating fixed by the forming field. The density of these "beads" must be about 0.3Ilc=3x102°cm -3. from laser prism Fig. 4 Scheme of proof-of-principle experiment The period of this structure should be in accordance with usual linac rule (6) 'Acl 2 =0.2J.lm. Only one wavelength A.=A.e is used in this case: inertia of the plasma ions gives the possibility to use this grating during a short time - 3 psec. The model consists of a beam splitter, 2 mirrors, 2 prisms and 2 lenses, which give a pair of intersecting beams. The dielectric grating ("beads" with a period -11./5) is placed at the point of beams crossing. The focal length of the lenses is -1m, the light beams width at the region of crossing is -lmm. The amplitude parameter must be qz '" 0.4, in order to have strong AG focussing. It gives the amplitude of field E m=ITV/m in the focal (crossing) region. Plane polarization of the laser field leads to one dimensional focussing instead of 2-dimensional, in the case of a cylindrical field, so we expect some defocussing in the 2nd direction; the principal effect will be present. Two-dimensional focussing may be realized by means of a second set of elements, as shown in Fig 4, but disposed in the orthogonal plane (y instead of x). The eXRected value of accelerating gradient is E.",100 kV/1I.=1O VIm, which corresponds to an energy gain in the focal region (-lmm) 100 MeV. 4 CONCLUSIONS Preliminary analytical and numerical studies of charged particles motion in the cylindrical field TMomn (<p,r,z) show the existence of deep (-keVs) 3-dimensional r.f. wells (h.f. traps), steady or moving, for electrons (positrons) at field densities - 1 MV/A.. Preliminary numerical studies of plasmoid dynamics confirm the above data up to the plasma densities -50% of the critical (oo=oop) value. Various schemes for the acceleration of positive ions, electrons and positrons by means of plasmoids, captured in r.f. wells, are discussed. Expected values of accelerating gradient are -100 ke V IA.. Two variants of experimental models are proposed: a section of accelerating structure (plasmoids grating in a tube with a diameter -lcm and length -6cm, e.m. field energy - 6J wavelengths 11.=20 and 40 J.lm, energy gain 300 MV, and a proof-of-principle experiment (dielectric "beads" grating, Nd-glass laser, energy -lJ, pulse length c't-lmm, energy gain -100 MV). 5 ACKNOWLEDGEMENTS This work was partially supported by the U.S. Department of Energy, Office of Energy Research, Office of High Energy and Nuclear Physics, under Contract No. DEA-AC03-76SF0098. The authors are thankful to M. Zolotorev for helpful discussions. One of the authors (A.LD.) is thankful to LBNL and to the International Science and Technology Center for support of this work. 6 REFERENCES [1] A.M. Sessler, "Collective-Field Acceleration", Proc. VII-th Int. Particle Accelerators Conf., Yerevan, 1969,2, 431 (1970). [2] E. Esarey, et al. IEEE Trans on Plasma Sci., 14, No.2, 252-288 (1996). [3] K. Shimoda, Applied Optics, 1,3 (1962). [4] H. Motz and c.J. H. Watson, "The radio-frequency confinement and acceleration of plasmas", Advances in Electronics, ed. by L. Marton, Acad. Press, New.y ark, N.Y. 153 (1967). [5] I.R. Gekker, " The Interaction of strong electromagnetic waves with plasmas", Clarendon Press, Oxford, 1982 (transl. from Russ.). [6a] A.1. Dzergach, Proc 4th European Particle Accelerator Conference, EPAC-94, YoU, 814-816. [6b] A.L Dzergach, V.S. Kabanov et aI, ibid., 811-813. [7] A.1. Dzergach, Europhys. Let. 29 (7) 525-530 (1995). [8] I.M. Finn. et al., " Physics of Plasmas" 4 (5), 1238-1248 (1997). [9] A.M. Sessler, Proc of the Workshop on Laser Acceleration of Particles, 1982, AlP Conf. Proc. 91, 154 (1982). [10] A.M. Sessler, E. Sternbach and J.S. Wurtele, Nucl Instrum. and Methods in Phys. Res. B-40/41, 1064-1068 . (1989). [11] K-J Kim, M Xie and A.M. Sessler, Nucl. Instr. a Method. in Phys. Res. A375 No. 1-3 (17th Int. FEL Cont). 523-525 (1996). [12] P. Morton and S. Chattopadhyay, Nucl. Instr. and Meth. in Phys. Res. A358, No. 1-3 (l6th Int. FEL Cont) 138-141 (1995). [13] N.S. Ginzburg et aI, IEEE Trans. on Plasma Sci. Vol 24, No.3, 770-780 (1996). [14] R.D. Boyd et aI, Applied Optics, 34, No. 10, 1697-1706 (1995). [15] B.W. Shore et aI, J. Opt. Soc. Am. NVol 14, No.5, 1124-1136 (1997). 3 @!;;J~lfiI;-Jij' ~ I!~W4;J3~1"* ®¥!I;;J:ilII=-Y3i1 ~ ~ ~ ~ U @)l!Ifl3l!1L@!\1o ~.lflm'4 ~ 

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About the Realization of Laser Acceleration Schemes Based on Plasmoids in R.F. Wells

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About the realization of laser acceleration schemes based on plasmoids in r.f. wells

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