Ion Bombardment In Rf Guns: Analytical Approach

Transcript

Ion Back-Bombardment in RF Guns Eduard Pozdeyev BNL with contributions from D. Kayran, V. Litvinenko, I. Ben-Zvi E. Pozdeyev 1 RF Photoguns with NEA Cathode • NEA GaAs photocahtodes: – High QE (unpolarized) – Polarization (lower QE) • RF Photoguns: – Good beam quality at high charge/bunch – Possibly, high average intensity (SRF) • Linac/ERL based applications: – – – – eRHIC and other Linac/ERL based colliders Electron coolers, conventional high(er) energy and coherent Light Sources and FELs Required beam currents > 100 mA! Polarization! E. Pozdeyev 2 Ion Bombardment in DC photoguns Achieved operational current and life time - DC, unpolarized: ~10 mA, ~500 C - DC, polarized: ~500 μA, ~500-1000 C Ion back-bombardment causes QE degradation of GaAs photocathodes A large portion of ions comes from the first few mm’s of the beam path. This problem is hard to overcome. anode Ionized residual gas strikes photocathode cathode E. Pozdeyev 3 Simulation of ion bombardment in RF guns Lewellen, PRST-AB 5, 020101 (2002) Ion bombardment in RF gunsis possible. Results are hard to interpret and extrapolate to other guns. Analytical model is needed for better insight! E. Pozdeyev 4 Ion in RF field Proposed by Kapitza (1951), Landau+Lifshitz (Mechanics, 1957), A. V. Gaponov and M. A. Miller (1958) – applied to EM Fields 1) q vB c r  x  a, x  r a – fast oscillating term mr  qE  q     m(x  a)  qE(x, t )  q (a  x )E  (x  a )  B(x, t ) c Fast, 0th – order in |a|/L 2) Method is applicable if | (a  )E || E |  | a | / L  1 Slow and Fast, 1th – order in |a|/L L ~ a few cm’s,  ~ 10-100 μm 3) Magnetic field is of the order | a | / L  1 1 B E   c t  vB a |a| E. Pozdeyev ~  (  E) ~ | E || E | c  L 5 Effective potential energy Assume : E(r , t )  Ε (r ) cos(t   ) 4) Fast oscillations (0th – order in |a|/L): ma  qE cos(t   )  qE sin( t   ) 2 qE cos(t   ) a   , a  c 2 mc mc2 5) Plugging 4) into 1) and average with respect to time yields: 2  c  q  2 x    2  |E | 4  mc  2 2  mc  q | E |  Ue   2  4  mc  2 | x |2 Te  m , 2 2 Ponderomotive force 2 Ee  TE.ePozdeyev  U e  const , L  Te  U e 6 Initial Velocity and Kinetic Energy Assume: • Ions produced by the beam only, • Ions originate with zero energy and velocity qE sin( t   ) mc2 qE sin( t   ) r0  0  x 0  c mc2 r0  x 0  a 0  x 0  c 2 | x 0 |2  2 mc 2  q | E |  2 2 Te 0  m  sin (  t   )  2 U sin (t   )   e 2 2 2  mc  Now the problem can be solved trivially. Important! x’0 depends on the RF phase when ionization happens. E. Pozdeyev 7 Axially symmetric geometry: on-axis motion E r  B  0, E z  0 - ion motion is 1D Solution of Ee  Te  U e  const Te  0 Electron acceleration force describes ion motion describes areas accessible to ions Facc  eE cos(t   ) qE sin( t   ) Initial effective ion velocity x 0  c , 2 mc -/2 <t+ <0, F and x’0 point in opposite directions 0 <t+ </2, F and x’0 point in the same direction This can be used to repel ions from ½-cell gun. E. Pozdeyev In multi-cell guns, cathode biasing can be used. 8 Ions originating close to cathode • Ions and electrons have charges of opposite signs • Ions accelerated towards cathode after ionization • Ions originating close to cathode can reach cathode on the first cycle • If not, they drift away (if phase is right) • The distance is smaller than double amplitude of fast oscil. Ion t 0 z E. Pozdeyev 9 Off-axis ion motion Electric field on the gun axis: Ea=Ez(z,r=0) U e ~ E 2 , E 2  E z2  E r2  E a2  2E aE z  E r2 E  1 E z ( z , r )  E a   E" a  2a r 2 4   E' a E r ( z, r )   r 2 Field off axis: 2 2 Effective potential E a  2 (E' a ) 2 2  mc  q   2 E a  Ue  r   2   E a   E" a  2 r  energy off-axis: 4  mc   2    4  Equation of motion: U e d L L  , 0  0  mr    Fr dt r r r E a  (E' a ) 2  mc  q     r Fr   2   E a  E" a  2   4  mc E.Pozdeyev   2    2 2 10 Off-axis ion motion: Cont’d If r << λ , r and z are decoupled Solve z-motion first, r-motion next using x’z on-axis 1) Numerical solution mr  Fr 2) Solve by iterations r  r0  r1 mr1  Fr (r0 ) ' Fr ( ' )d ' d "  dr  x z 0d r1 ( z  0)       mx z ( ' ) 0 x z ( " )  dz 0 0 x z ( ) 0 z0 E. Pozdeyev z0 11 BNL 1/2-cell SRF Gun fRF = 703.75 MHz Emax = 30 MeV/m (on axis) Energy = 2 - 2.5 MeV Iav = 7-50 mA (0.5 A) qb = 0.7-5 nC fb = 10 MHz (up to 700 MHz) SuperFish File Gun 5cm Iris NO transition Section F = 703.68713 MHz 18 18 16 16 14 14 12 12 10 10 8 8 6 6 4 4 2 2 E. Pozdeyev 0 0 0 5 10 15 20 C:\DOCUMENTS AND SETTINGS\KAYRAN\MY DOCUMENTS\ERL\SCGUN_DESIGN\FROM_RAM\RGUN51.AM 4-25-2005 25 10:50:06 =0 12 BNL Gun: On-axis motion Beam phase was calculated using PARMELA Beam RF phase E. Pozdeyev 13 BNL Gun: off-axis motion rcathode  r0 vs. ionization coordinate r0 E. Pozdeyev 14 Comparison to a DC gun Common: p=5·10-12 Torr BNL ½-cell Gun: E=2 MeV, Ions come from z<3.36 (E~750 keV)  dN     1.7 106 ions/C  dQ  RF , BNL HV DC Gun: Gap = 5 cm, V=650 kV  dN     2.4 106 ions/C  dQ  DC The number of ions in the BNL gun can be reduced by a factor of 5 by (im)proper phasing of the gun (accelerate in phase range 0<t+</2) E. Pozdeyev 15 Conclusions • Ion bombardment is possible in RF guns • Ions move in the effective potential field  2 mc2  q | E |  Ue   2  4  mc  2 • RF phase of the beam defines the effective initial velocity and kinetic energy qE sin( t   ) x 0  c mc 2 Te  2U e sin 2 (t   ) • Ions move towards the cathode if acc. voltage is growing and from the gun if Vacc is going down. => It is possible to repel most of ions from a ½ -cell gun by a proper phasing. • Ions from the very close vicinity (~50 μm) still will be able to bombard the cathode. This limits gain to DC guns to ~ 10. • Phasing will not work in multi-cell guns. Cathode can be biased to a 100’s V – 1 kV. • Ions cannot penetrate from outside. No biased electrodes needed. E. Pozdeyev 16