Transcript Ion Bombardment in RF Guns: Analytical Approach

Ion Back-Bombardment in RF Guns
Eduard Pozdeyev
BNL
with contributions from
D. Kayran, V. Litvinenko, I. Ben-Zvi
E. Pozdeyev
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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
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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
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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
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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|
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~  (  E) ~
| E || E |
c

L
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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
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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.
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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.
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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
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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
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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
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z0
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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
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C:\DOCUMENTS AND SETTINGS\KAYRAN\MY DOCUMENTS\ERL\SCGUN_DESIGN\FROM_RAM\RGUN51.AM 4-25-2005
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=0
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BNL Gun: On-axis motion
Beam phase
was calculated
using PARMELA
Beam RF phase
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BNL Gun: off-axis motion
rcathode  r0
vs. ionization coordinate
r0
E. Pozdeyev
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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)
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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
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