Lecture 5: Photoinjector Technology J. Rosenzweig UCLA Dept. of Physics & Astronomy USPAS, 7/1/04
Lecture 5: Photoinjector
Technology
J. Rosenzweig
UCLA Dept. of Physics & Astronomy
USPAS, 7/1/04
Technologies
• Magnetostatic devices
– Computational modeling
– Map generation
• RF cavities
– 2 cell devices
– Multicell devices
– Computational modeling: map generation
• Short pulse lasers
• Diagnosis of electron beams
The photoinjector layout
ORION gun side view
SPARC gun and solenoid
Solenoid Design
• Electromagnet with iron yoke and field stiffeners/dividers
• Iron acts as magnetic equipotential.
• Use of magnetic circuit analogy for dipole gives field strength
ORION design has all coils in series
SPARC design has four independent coils
r H •d
r l = Ienc
B0
µ0Lsol +
1
µ
r B • d
r l
Fe
= IencB0 µ0NI /Lsol
Solenoid field tuning
• No motion of heavy solenoid
• Uniform field possible
• Tune centroid of emittance
compensation lens by
asymmetric excitation of the
four coils
• Simulation indicates 8 G
field at cathode.
0
1000
2000
3000
4000
5000
10 20 30 40 50 60
UniformDown rampUp ramp
B (
G)
z (cm)
Maps available for HOMDYN
Ramp up field Ramp down field
Effect of solenoid tuning on
beam dynamics
• Beam dynamics studied with HOMDYN
• SPARC/LCLS design surprisingly robust, may be fine-
tuned using this method
0
0.5
1
1.5
2
2.5
3
3.5
0 1 2 3 4 5 6 7 8
Sigma (ramp down)Emittance (ramp down)Emittance (flat)Sigma (flat)
[mm]
[mm-mrad]
z [m]
Other emittance compensation
solenoid designs• Lower gradients are
possible for integratedphotoinjectors
• Lower magneticfocusing fields as well
• Fields closer to thecathode for beamcontrol
• “Bucking” coil needed
• Example: PEGASUSPWT injector
z
Field null at cathode
Main coilBucking coil
Other solenoids: linac emittance
compensation• In TW linac, second
order RF focusing is notstrong
• Generalize focusing inenvelope equation
• Example: for 20 MV/mTW linac,
=1 (pure SW),
= 0 (pure TW), = 0.4 (SLAC TW)
+ 2b2, b = cB0 /E0
for b2 =1, B0 =1.1 kGSPARC linac solenoid, From LANL POISSON
Some practical considerations
• Power dissipation limited. Limit is roughly
700 A/cm2 in Cu
• Yoke saturation: avoid fields above 1 T in
the iron
=r B •d
r A
pole
AFe >> ApoleBpoleBsat
c = 5.8 105 cm( )-1( )
dP
dV=J 2
c
1 W/cm3
RF structures
• Photoinjectors are based
on high gradient standing
wave devices
• Need to understand:
– Cavity resonances
– Coupled cavity systems
– Power dissipation
– External coupling
• Simple 2-cell systems to
much more elaborate
devices… UCLA photocathode gunwith cathode plate remove
The “standard” rf gun
• Concentrate on simplest case
• -mode, full ( /2) cell with 0.6 cathode cell
• Start with model
Cavity resonances
Lz
Rc
• Pill-box model approximates
cylindrical cavities
• Resonances from Helmholtz
equation analysis
• Fields:
• Stored energy
0,1
2.405c
Rc
1
kz, n
2+
2
c2
˜ R = 0
No longitudinal dependencein fundamental
Ez( ) = E0J0 k ,0( )
H ( ) = 0
k ,0
E0J1 k ,0( ) = c 0E0J1 k ,0( )
UEM = 14 0LzE0
2 J02 k , 0( ) + J1
2 k , 0( )[ ] d0
RC
= 12 0LzE0
2Rc2J1
2 k , 0RC( )
A circuit-model view
• Lumped circuitelements may beassigned: L, C, and R.
• Resonant frequency
• Tuning by changinginductance,capacitance
• Power dissipation bysurface current (H)
Contours of constantflux in 0.6 cell of gun
1
LC
Cavity shape and fields
• Fields near axis (in iris region) may be betterrepresented by spatial harmonics
• Higher (no speed of light) harmonics havenonlinear (modified Bessel function) dependenceon .
– Energy spread
– Nonlinear transverse RF forces
• Avoid re-entrant nose-cones, etc.
Ez( ,z ,t) = E0 Im ann=
exp i kn, zz t( )[ ]I0 k , n[ ] k , n = kn, z2 / c( )
2
Power dissipation and Q
• Power is lost in a narrow layer (skin-depth) of the
wall by surface current excitation
• Total power
• Internal quality factor
• Other useful interpretations of Q
dP
dA=
Ks2
4 s c
=Ks2
4
µ 0
2 c
=Ks2
2Rs ,
Rs1
2
µ 0
2 c
Ks =
r H || = µ 0
r B ||
Surface resistivity
Surface current
QUEM
P=Z02Rs
2.405LzRc + Lz( )
P = Rs c 0E0( )2RcLzJ1
2 k , 0Rc( ) + 2 J12 k , 0( ) d
0
Rc
= Rs c 0E0( )2RcJ1
2 k , 0Rc( ) Lz + Rc[ ]
Z0 = 377
Q = f =1/ 2
=L
R
Cavity coupling
• Circuit model allowssimple derivation of modefrequencies
• Solve eigenvalue problem
• Mode separation isimportant
• In 1.6 cell gun
(b)L
C
LC
CC
z
Electric
coupling
(a)
= 0 (0 - mode) and = 0 1+ 2 c ( - mode)
d2I1dt2
+ 02 1 c( )I1 = c 0
2I2
d2I2dt2
+ 02 1 c( )I2 = c 0
2I1
c >> 0/Q
f = 3.3 MHz, f = 2856 MHz, Q =12,000
Measurement of frequencies
• Frequency response can be measured on a network analyzer
• Resonance frequencies of individual cells and coupled modes
• Tuning via Slater’s theorem guide
Reflection measurement S11(5-cell deflection mode cavity)
0
0
=Vc
UEM
12 0
r E 2 1
2 µ 0
r H 2[ ]
Width of resonances measures Q.
Measurement of fields
• Use so-called “bead-pull”
technique
• Metallic of dielectric bead (on
optical fiber)
• Metallic bead on-axis gives
negative frequency shift
(electric field energy
displaced)
• More complex if one has
magnetic fields (deflector)0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 2 4 6 8 10
Neptune Gun Bead Pull
DataSuperfish balancedSuperfish x 1.04 in 0.6 cell
Fiel
d am
plitu
de s
quar
ed
z [cm]
Ez
Temporal response of the cavity
• Standing wave cavity fillsexponentially
• Gradual matching ofreflected and radiatepower (E2) from inputcoupler
• In steady-state, all powergoes into cavity (criticalcoupling)
• Ideal VSWR is 1 (no beamloading)
0.0
0.20
0.40
0.60
0.80
1.0
0 1 2 3 4
Cavity PowerReflected power
Rel
ativ
e po
wer
t/f
E 1 exp( /2Q)
Reading references
• Magnets: Chapter 6, section 2
• RF cavities: Chapter 7, sections 2-8