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 SPARC gun and solenoid ORION gun side view
Solenoid Design SPARC design has four independent coils ORION design has all coils in series Electromagnet with iron yoke and field stiffeners/dividers Iron acts as magnetic equipotential. Use of magnetic circuit analogy for dipole gives field strength r H d r B l = I 0 enc L sol + 1 r B d r l = I enc B 0 µ 0 NI /L sol µ 0 µ Fe
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. B (G) 5000 4000 3000 2000 1000 Uniform Down ramp Up ramp 0 10 20 30 40 50 60 z (cm) Maps available for HOMDYN Ramp up field Ramp down field
Effect of solenoid tuning on beam dynamics 3.5 3 2.5 Sigma (ramp down) Emittance (ramp down) Emittance (flat) Sigma (flat) 2 [mm] [mm-mrad] 1.5 1 0.5 0 0 1 2 3 4 5 6 7 8 z [m] Beam dynamics studied with HOMDYN SPARC/LCLS design surprisingly robust, may be finetuned using this method
Other emittance compensation solenoid designs Lower gradients are possible for integrated photoinjectors Lower magnetic focusing fields as well Fields closer to the cathode for beam control Bucking coil needed Example: PEGASUS PWT injector Bucking coil Main coil Field null at cathode z
Other solenoids: linac emittance compensation In TW linac, second order RF focusing is not strong =1 (pure SW), = 0 (pure TW), = 0.4 (SLAC TW) Generalize focusing in envelope equation SPARC linac solenoid, From LANL POISSON + 2b 2, b = cb 0 / E 0 Example: for 20 MV/m TW linac, for b 2 =1, B 0 =1.1 kg
Some practical considerations Power dissipation limited. Limit is roughly 700 A/cm 2 in Cu Yoke saturation: avoid fields above 1 T in the iron = dp dv = J 2 c 1 W/cm 3 pole r B da r A Fe >> A pole B pole B sat ( c = 5.8 10 5 ( cm) -1 )
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 gun with 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 R c L z Pill-box model approximates cylindrical cavities Resonances from Helmholtz equation analysis 1 k 2 z, n + 2 R c = 0 2 No longitudinal dependence in fundamental Fields: E z H ( ) ( )= E 0 J 0 k,0 Stored energy 0,1 2.405c R c ( )= 0 E 0 J 1 ( k,0 )= c 0 E 0 J 1 ( k,0 ) k,0 U EM = 1 4 0L z E 0 2 R C [ J 2 0 ( k,0 )+ J 2 1 ( k,0 ) ] d 0 ( ) = 1 L E 2 2 0 z 0R 2 c J 2 1 k,0 R C
A circuit-model view Lumped circuit elements may be assigned: L, C, and R. Resonant frequency 1 LC Tuning by changing inductance, capacitance Power dissipation by surface current (H) Contours of constant flux in 0.6 cell of gun
Cavity shape and fields Fields near axis (in iris region) may be better represented by spatial harmonics E z (,z,t) = E 0 Im a n exp[ ik ( n, z z t) ]I 0 [ k, n ] k, n = k 2 n, z ( / c) 2 n= Higher (no speed of light) harmonics have nonlinear (modified Bessel function) dependence on. Energy spread Nonlinear transverse RF forces Avoid re-entrant nose-cones, etc.
Power dissipation and Q Power is lost in a narrow layer (skin-depth) of the wall by surface current excitation dp da = K 2 s = K s 4 s c 4 Total power Internal quality factor 2 Q U EM P µ 0 2 c = K 2 s P = R s c 0 E 0 = Z 0 2R s 2 R s, R s 1 2 2.405L z ( R c + L z ) K s = Other useful interpretations of Q µ 0 2 r c r H = µ 0 B ( ) 2 R c L z J 2 1 k,0 R c Surface resistivity Surface current R c ( )+ 2 J 2 1 ( k,0 ) d 0 = R s ( c 0 E 0 ) 2 R c J 2 1 ( k,0 R c ) L z + R c [ ] Z 0 = 377 Q = f = 1/2 = L R
Cavity coupling (a) z Electric coupling Circuit model allows simple derivation of mode frequencies d 2 I 1 dt + 2 2 0( 1 c )I 1 = c 2 0 I 2 d 2 I 2 dt + 2 2 0( 1 c )I 2 = c 2 0 I 1 Solve eigenvalue problem (b) L C C C = 0 (0 - mode) and = 0 Mode separation is important c >> 0 /Q 1+ 2 c ( - mode) L C In 1.6 cell gun 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 = V c r 2 0E 2 1 µ r 2 0H 2 0 0 U EM 1 [ ] Reflection measurement S 11 (5-cell deflection mode cavity) Width of resonances measures Q.
Measurement of fields Field amplitude squared 1.4 1.2 1 0.8 0.6 0.4 0.2 0 Neptune Gun Bead Pull Data Superfish balanced Superfish x 1.04 in 0.6 cell 0 2 4 6 8 10 z [cm] 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) E z More complex if one has magnetic fields (deflector)
Temporal response of the cavity Relative power 1.0 0.80 0.60 0.40 0.20 0.0 0 1 2 3 4 t/ f Cavity Power Reflected power Standing wave cavity fills exponentially E 1 exp( /2Q) Gradual matching of reflected and radiate power (E 2 ) from input coupler In steady-state, all power goes into cavity (critical coupling) Ideal VSWR is 1 (no beam loading)
Reading references Magnets: Chapter 6, section 2 RF cavities: Chapter 7, sections 2-8