E. Pozdeyev1 Ion Back-Bombardment in RF Guns Eduard Pozdeyev BNL with contributions from D. Kayran,...
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Transcript of E. Pozdeyev1 Ion Back-Bombardment in RF Guns Eduard Pozdeyev BNL with contributions from D. Kayran,...
E. Pozdeyev 1
Ion Back-Bombardment in RF Guns
Eduard Pozdeyev BNL
with contributions from D. Kayran, V. Litvinenko, I. Ben-Zvi
E. Pozdeyev 2
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 3
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
cathodeIonized residual gas strikes photocathode
anode
A large portion of ions comes from the first few mm’s of the beam path.This problem is hard to overcome.
E. Pozdeyev 4
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 5
Ion in RF fieldProposed by Kapitza (1951), Landau+Lifshitz (Mechanics, 1957), A. V. Gaponov and M. A. Miller (1958) – applied to EM Fields
BvEr c
qqm
1/|||||)(| LaEEa L ~ a few cm’s, ~ 10-100 μm
),()()(),()( tc
qqtqm xBaxEaxEax x
1)
2)
rxaxr , a – fast oscillating term
Method is applicable if
Magnetic field is of the order 1/|| La
tc
BE
1 ||||||
~)(~ EEa
EaBv
Lc
3)
Fast, 0th – order in |a|/L Slow and Fast, 1th – order in |a|/L
E. Pozdeyev 6
Effective potential energy
Fast oscillations (0th – order in |a|/L):
222 )sin(
,)cos(
)cos(
mc
tqc
mc
tq
tqm
EE
E
aa
a
2
2
22 ||
4
mc
qmcU e
E
4)
5) Plugging 4) into 1) and average with respect to time yields:
22
2
22
||4
E
mc
qcx
)cos()(),( :Assume trtr ΕE
Ponderomotiveforce
eeeeee UTLconstUTEmT ,,2
|| 2x
E. Pozdeyev 7
Initial Velocity and Kinetic Energy
Assume: • Ions produced by the beam only,• Ions originate with zero energy and velocity
200
20000
)sin(0
)sin(
mc
tqc
mc
tqc
E
E
xr
xaxr
)(sin2)(sin||
22
|| 222
2
2220
0
tUt
mc
qmcmT ee
Ex
Now the problem can be solved trivially. Important! x’0 depends on the RF phase when ionization happens.
E. Pozdeyev 8
Axially symmetric geometry:on-axis motion
0,0 zr EBE
0eT describes areas accessible to ions
constUTE eee Solution of describes ion motion
Electron acceleration force )cos( teacc EF
,)sin(
20 mc
tqc
ExInitial effective ion velocity
-/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. In multi-cell guns, cathode biasing can be used.
- ion motion is 1D
E. Pozdeyev 9
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.
z
t
0
Ion
E. Pozdeyev 10
Off-axis ion motionElectric field on the gun axis: Ea=Ez(z,r=0)
Field off axis:
rrz
rrz
ar
aaaz
2),(
4
1),( 2
2
E'E
EE"EE
Effective potential energy off-axis:
2
22
22
2
2
2 )(
24rr
mc
qmcU aa
aa
ae 4
E'EE"
EE
Equation of motion:
rmc
qmcF
Fr
Urm
r
L
r
L
t
aaaar
re
2
)(
4
0,d
d
2
2
2
2
2
0
E'EE"E
222222 2 rzaarzeU EEEEEEE,E~
E. Pozdeyev 11
Off-axis ion motion: Cont’d
If r << λ , r and z are decoupledSolve z-motion first, r-motion next using x’z on-axis
1) Numerical solution
rFrm
2) Solve by iterations
)( 0110 rFrmrrr r
00
0
0
00
'
0
1 )(
d
d
d
)"(
"d
)'(
'd)'()0(
z
z
z
z
zz
r
x
x
z
r
xxm
Fzr
E. Pozdeyev 12
BNL 1/2-cell SRF Gun
SuperFish File Gun 5cm Iris NO transition Section F = 703.68713 MHz
C:\DOCUMENTS AND SETTINGS\KAYRAN\MY DOCUMENTS\ERL\SCGUN_DESIGN\FROM_RAM\RGUN51.AM 4-25-2005 10:50:06
0
2
4
6
8
10
12
14
16
18
0
2
4
6
8
10
12
14
16
18
0 5 10 15 20 25
fRF = 703.75 MHzEmax = 30 MeV/m (on axis)Energy = 2 - 2.5 MeVIav = 7-50 mA (0.5 A)qb = 0.7-5 nCfb = 10 MHz (up to 700 MHz)
=0
E. Pozdeyev 13
BNL Gun: On-axis motion
Beam RF phase
Beam phasewas calculated using PARMELA
E. Pozdeyev 14
BNL Gun: off-axis motion
vs. ionization coordinate0
0
r
rrcathode
E. Pozdeyev 15
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)
HV DC Gun: Gap = 5 cm, V=650 kV
ions/C 104.2 6
DCdQ
dN
ions/C 107.1 6
,
BNLRFdQ
dN
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 16
• Ion bombardment is possible in RF guns
• Ions move in the effective potential field
• RF phase of the beam defines the effective initial velocity and kinetic energy
• 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.
Conclusions
2
2
22 ||
4
mc
qmcU e
E
20
)sin(
mc
tqc
Ex )(sin2 2 tUT ee