1. High Efficiency X-band Klystron Design Study
Brandon Weatherford, Rich Kowalczyk, Valery Dolgashev, and Jeff Neilson – SLAC National Accelerator Laboratory
Aaron Jensen – Leidos, Inc.
Igor Syratchev, Jinchi Cai and Walter Wuench - CERN
Jan. 24, 2018

2. Agenda
Program overview
Design targets
Core Oscillation Method
Bunching circuit design
Multi-gap output cavity optimization
Conclusions

3. High Efficiency X-band Design Study - Overview
SLAC/CERN collaboration funded by CERN to explore achievable efficiencies for high peak power X-band klystron
Use recently developed techniques to improve existing SLAC XL series 50 MW, 38% efficient klystron
Improve efficiency with novel bunching techniques such as Core Oscillation Method (COM)
Improve output cavity lifetime using based on lessons learned from design and test of high gradient structures
Performance targets:
Frequency: 12 GHz
Pulse Width: 2 µs
Efficiency: >70 percent
Peak RF Power: 40 MW minimum, 50MW goal

4. Design Study Plan
Preliminary COM bunching circuit designs in 1D AJDisk
Effect of perveance
Fill Factor
Klystron length
Intermediate design with 2D large signal codes (KlyC, TESLA)
Radial effects
Benchmarking of KlyC vs. MAGIC/VSIM vs. TESLA
Output cavity designs in MAGIC-2D done in parallel with bunching circuit design
Standing wave and travelling wave designs
Evaluate for efficiency and peak surface fields
Final design on PIC codes (MAGIC,VSIM)
Stability analysis
Include calculations for depressed collector

5. Design Challenges Minimizing radial stratification effects
Ultimate efficiency is limited, in part, by radial variation in beam interaction with klystron cavities
Generating optimal velocity distribution in fully saturated beam at the output
How do we slow down all electrons to the same energy after the output gap?
Given some energy spread, optimize the velocity profile of the incoming bunch
Existing XL klystron is already limited by high gradients in output cavity; even larger gradients will arise in a high-efficiency design
Increase output circuit length
Evaluate standing and traveling wave configurations
Consider distributed RF power extraction

6. Core Oscillation Method (COM) Klystron Design
Preliminary 1-D COM klystron designs are developed in AJDisk.
Assume an “ideal” output cavity (M = 0.9) and optimize bunching circuit.
Applegate Diagram
3x bunching cavities
7x “oscillation” cavities
Fundamental & Second Harmonic Current
0.9 μK, 66% Fill Factor
11 Cavities 
81.9% RF Efficiency in AJDisk
Electron Velocities

7. KlyC-2D Simulation: 0.9 uK, 11 Cavity Design
0.9 μK, 66% Fill Factor
11 Cavities
3.4% degradation in efficiency due to 2D effects. Simulated RF efficiency is 78.5%.
10-Layer model:
Radial Stratification = 1.67
Spent Beam Velocity = 0.42c (outer) to 0.67c (inner)

8. Results - Variable Perveance, Fill Factor
Design
0.9 μK, 75% FF
0.9 μK, 66% FF
1.5 μK, 66% FF
Efficiency (%)
79.4*
78.5
72.6
r Stratification
1.32
1.67
1.73
Maximum I1/I0
1.83
1.84
1.82
Spent e- velocity
0.44 – 0.59
0.42 – 0.67
0.41 – 0.65
*For 75% FF, further improvement may be possible with fine-tuning of the output cavity

9. Results – 9 Cavities vs. 11 Cavities
11-Cavity klystron appears too long. Outer electrons start de-bunching before output; however, inner electrons continue to bunch
9-cavity klystron was modeled as well: only a 2.5% drop in efficiency, to 76.0%
11 Cavities:
805 mm Length
78.5%
9 Cavities:
670 mm Length
76.0%

10. Efficiency vs. Output Circuit
Efficiency strongly depends on the gap coupling factor, M, of the output cavity
Impact of output cavity (M = 0.7, 0.75) was modeled in AJDisk (left)
> 70% efficiency target was achieved in KlyC-2D with M = 0.75
XL-4 M value is approximately 0.8 – this is an achievable design!
Optimization using KlyC-2D may yield a few % improvement
AJDisk (1D) output tuning
KlyC-2D: 70.7% efficiency
No reflected electrons

11. Bunching Circuit - Summary
KlyC-2D simulations show that with a realistic output cavity, we can expect to reach a 70% efficient klystron design.
Multiple high efficiency COM topologies have been explored
Moving forward, output cavity design is most critical
Efficiency may further be increased by:
Re-optimization of bunching circuit with M=0.75 output
Raising beam voltage (reducing perveance), within reason
Using superconducting magnets
Design
# Cavities
Beam Voltage
Beam Current
Output Power
Efficiency
XL-4 7
420 kV
335 A
~ 50 MW
~ 38%
0.9 µK COM
9 – 11
363 kV
197 A
> 50 MW
> 70%

12. Multi-gap Output Circuit – Existing XL-4 Design
119º
0.7π
88º
0.5π
117º
0.6π
MAGIC-2D used to model the standard XL-4 multi-gap output cavity
Imported beam from XL-4 klystron simulation
TW circuit, with variable phase advance
Beam parameters: 420 kV, 335 A
Efficiency = 38%
Gradient = 72 MV/m
π/2 mode = 0.5π
115 kV
120 kV
104 kV
115 kV
Maximum gradient in MAGIC simulation is 72 MV/m
Location depends on phase

13. Output circuit optimization set up w/ parameterized model: Two goals:
Axial taper (β)
Radial taper (α)
Cavity tuning (h)
Two goals:
Maximize RF efficiency, using standard XL-4 beam import
Minimize surface fields d0
d1=βd0
d2=βd1 h
r1=αr0
r2=αr1
r3=αr2 r0

14. Comparison of 2-Gap and 4-Gap Circuits
Results show that output efficiency can increased
Can we re-shape cells to minimize surface gradient?
Distributed power extraction may be particularly effective
4 Cell
2 Cell
4 Cell, extraction from each cell
Output circuit total length held roughly fixed at original 4 cell design

15. 4 Cell, 58% Efficient, 220 MV/m Excited by Beam
Extreme example gives 58% efficiency at 220 MV/m using poorly-bunched beam from the standard XL-4
Peak gradient in second cell is due to RF circuit impedance (i.e. a mismatch), not beam impedance
We could lower the gradient by choosing a more appropriate cell pattern to eliminate mismatch
Excited in first cavity
Power Flow

16. Output Circuit – Next Steps
End goal is to design the output circuit using a “COM-like” bunched beam instead of the XL-4 beam
MAGIC-2D model of 0.9 μK klystron has been constructed, results are forthcoming
Beam from MAGIC model will be exported, and used for output cavity optimization (also in MAGIC)
“Cold” RF field distribution from the optimized output circuit can be imported into KlyC or TESLA, and iterated upon for even more improvement in efficiency.

17. Conclusions
KlyC-2D simulations predict an efficiency of at least 70 percent with a realistic output circuit.
Efficiency of XL-4 traveling wave output circuit can be increased, based on 2-D PIC simulations
Next steps: optimization of output circuit (TW, SW, and distributed coupling) using imported COM beam from MAGIC-2D
Many thanks to CERN for supporting this development effort.
We are here. Onward and upward!