Lecture 5: Photoinjector Technologypbpl.physics.ucla.edu/Education/Schools/USPAS_2004/Lecture5.pdfBucking coil Main coil. Other solenoids: linac emittance compensation • In TW linac,

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