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