1. Towards more efficient klystron designs
Chiara Marrelli
TIARA workshop
Uppsala,18/6/2013

2. Introduction: motivation and main design guidelines
Klystron simulations and optimization with disk code
Cavity RF design
PIC simulations
Output cavity study
Conclusions
Chiara Marrelli

3. Introduction and motivations
From CLIC CDR (2012)
CLIC drive beam 3 TeV:
The average RF power at the accelerating structure input is
174 MW with challenging specifications in terms of stability:
± 0.05° in phase
0.2% in amplitude
Very high efficiency sources needed to provide this power at affordable cost (efficiency>70%)
Multibeam Klystrons proposed:
15 MW output power with small current per beamlet low perveance – good efficiency (state-of-the-art around 65%)
“multibeam” cavities: all beams interact in the same cavities
Chiara Marrelli

4. Introduction R&D on single beam device:
Single beam klystrons may have advantages in terms of reliability and phase noise
Efficiency pushed through:
very low perveance (<0.25)
careful optimization of the cavity parameters (easier on single beam cavities)
use of higher harmonic bunching cavities (2nd and 3rd)
Low perveance low output power clustered klystrons
Example (presented by S. Tantawi during last CLIC workshop - Jan. 2013):
16 beams
Chiara Marrelli

5. High efficiency klystron for CLIC
Perveance: K=I0/V03/2
Perveance determines to a large extent the power conversion efficiency.
The RF output current due to the input modulating voltage is maximum when the klystron transconductance g is maximum (g=Iout/Vin ∝ b’/K1/2 where b’ is the normalized beam radius and K the perveance).
It has been shown [*] that g is maximum for an optimized beam radius when the perveance is at a minimum. High efficiency klystrons (> 70 %) therefore require low perveance. [**]
Chosen parameters:
η = xK – I. Syratchev
η = xK - Thales
I0=8.21 A
V0=115 kV
P= 0.21
[*]R. R. Warnecke and P. R. Guenard, Tubes A Modulation De Vitesse, Paris, Gauthier-Villars, 1951
[**] E. Jensen, I. Syratchev, CLIC 50 MW L-Band Multi-Beam Klystron, 2005
Chiara Marrelli

6. High efficiency klystron for CLIC
Already in the 40s Guénard et al. suggested that if an electron beam could be bunched with a sawtooth voltage it should be possible to arrange matters so that nearly all the electrons passing through the input cavity within one cycle arrive together at the output gap.
In a simplified model efficiency can be also expressed as:
[*]
τ(φ)=electron transit time from input to output
Maximum η for τ(φ) periodic function of φ (sawtooth):
n= η ≈ 0.58
n= η ≈ 0.73
n= η ≈ 0.80
n= η ≈ 0.83
[*] R. Warnecke, J. Bernier, P. Guénard, “Groupement et dégroupement au sein d’un faisceau cathodique injecté dens un espace exempt de champs extérieurs après avoir été modulé dans sa vitesse”.
Chiara Marrelli

7. High efficiency klystron for CLIC: AJDisk simulations
1 D code currently used at SLAC for the design of round and sheet beam klystrons;
The beam is splitted into a series of disks of charge moving only in the longitudinal
direction;
Disks are acted by both the cavity fields and the space charge fields;
It can’t simulate traveling wave output structures.
AJDisk outputs:
Cavity complex voltages
Beam current (amplitude and phase) in the cavities
Particles minimum β
Gain
Efficiency
Maximum output electric field
Chiara Marrelli

8. High efficiency klystron for CLIC: AJDisk simulations
Main parameters
Nr of disks 50
Nr steps 32
Nr iterations(max) 70
Io(A):
Vo(kV):
f(MHz):
Pin(W):
Beam radius b (mm):
Fill Factor:
Perveance (uK):
v/c:
BetaE(rad/m):
Lambda(m):
LambdaP(m):
Cavity RQ(ohms) M Qe Qo f(MHz) z(cm) Harmonic
Single gap cavity
Chiara Marrelli

9. High efficiency klystron for CLIC: AJDisk simulations
Kinetic efficiency
Efficiency ( Electric ) =
Efficiency ( Kinetic ) =
Efficiency ( Total ) =
Electric efficiency
Chiara Marrelli

10. High efficiency klystron for CLIC: AJDisk simulations
** FOURIER COMPONENTS AND PHASES OF INDUCED CURRENT **
Cavity DC Component st Harmonic nd Harmonic rd Harmonic th Harmonic
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) ( )
********************** Simulated Power by Cavity ********************
Cavity Pexternal (kW) Pohmic (kW) Pohmic/A (kW/cm^2)
Sum
Cavity Voltages
Simulated Analytic
Cavity V(kV) Phase(deg) V(kV) Phase(deg)
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
( ) ( )
Min v/c:
z (Min v/c): m
Max I1/I0:
z (Max I1/I0): m
Gain (dB):
Output Max E-Field (kV/cm):
Chiara Marrelli

11. Cavity RF design First design using SUPERFISH to get:
R/Q
Coupling coefficient
frequency
3D Simulation with HFSS and study of high order modes possibly excited by the beam
Design of input coupler using HFSS
Input cavity with coupler:
Coupler: standard L-band waveguide WR770
Qext=485
R/Q=180
f=1000 MHz
M=0.94
Chiara Marrelli

12. Cavity RF design Second cavity (1005 MHz): Idler cavities:
9.25
1.1
R/Q=211
f=1005 MHz
M=0.938
Q=9464
Third cavity (1981 MHz):
6.37
3.4
TM mode at 5 GHz to be
shifted in previous design
R/Q=102
f=1981 MHz
M=0.85
Q=15300
Chiara Marrelli

13. Cavity RF design Fourth cavity (2983 MHz): Fifth cavity (1011 MHz):
4.76
3.5
R/Q=118
f=2983 MHz
M=0.885
Q=12300
Fifth cavity (1011 MHz):
11.38
2.65
From HFSS:
R/Q=84
f=1011 MHz
M=0.936
Q=17408
Chiara Marrelli

14. Time domain and Particle In Cell simulations
GdfidL simulations
Time domain and Particle In Cell simulations
Time domain (input cavity):
Tuning of input cavity: since we can’t use ports in eigenmode simulation (PEC on the port) frequency is checked in TD simulation by loading the eigenmode field and letting it ring
Calculation of external Q from field decaying: t1 t2 P1 P2
Particle In Cell (all cavities):
Simulation of the complete interaction between particles and cavities, transient and beam focusing
Chiara Marrelli

15. GdfidL PIC simulations
Setup of PIC simulation with GdfidL:
LOSSES: GdfidL doesn’t simulate losses in copper; loss mechanisms have to be introduced in cavities and pipes (to avoid high frequency modes excited by the beam – pipe is closed at the end)
TUNING: mesh can’t be reduced too much to keep the computing time reasonable. Keeping the same geometry simulated in HFSS for cavities means that we are off in frequency: for this reason tuners have to be introduced and the geometry has also to be modified a bit; this means that we can’t import the geometry from HFSS but build the whole structure point-by-point
Chiara Marrelli

16. 14.3 GHz mode excited in the pipe by the beam
GdfidL PIC simulations
First set of simulations with GdfidL (input cavity only):
running on one single machine (8 cores)
large mesh (2 mm)
simulation time ~ 1 week (for t=10 μs)
Example: input cavity with coupler (without any damping mechanism)
Gap voltage
f1= 1 GHz
f2≈ 14.3 GHz
f= 1 GHz
14.3 GHz mode excited in the pipe by the beam
Chiara Marrelli

17. GdfidL PIC simulations
Input cavity with coupler - PIC
Damping rings on the pipe:
To damp high frequency modes excited by the beam in the pipe (closed at the end)
we introduce Mkappa (magnetic conductivity)
in the cylinder material.
Losses are due to orientation of magnetic dipoles
(magnetic current - variations of B)
Tuner+losses inside the cavity:
μr slightely different from 1 (to change frequency)
mkappa to introduce ohmic losses
Chiara Marrelli

18. GdfidL PIC simulations
Input + idler cavities and dampers
Shot @ t= 9.9 μs
running on one single machine through LSF (8 cores) – GdfidL version ” ”
mesh 1.25 mm
timestep= e-12 s
20 particles emitted per timestep
simulation time ~ 1 week (simulated time = 10 μs)
longitudinal constant B field = 0.07 T
Chiara Marrelli

19. GdfidL PIC simulations
Voltage as a function of time and frequency in cavities
Input cavity
GdfidL:
Peak voltage ~ 6.8 kV
From AJDisk:
Peak voltage = 6.2 kV
Second cavity (1005 MHz)
GdfidL:
Peak voltage ~ 20 kV
From AJDisk:
Peak voltage =17.5 kV
Chiara Marrelli

20. GdfidL PIC simulations
Third cavity (1981 MHz)
GdfidL:
Peak voltage ~ 18 kV
From AJDisk:
Peak voltage = 18.7kV
Fourth cavity (2983 MHz)
GdfidL:
Peak voltage ~ kV
From AJDisk:
Peak voltage = 9.5 kV
Chiara Marrelli

21. GdfidL PIC simulations
Fifth cavity (1011 MHz)
GdfidL:
Peak voltage ~ 35 kV
From AJDisk:
Peak voltage = 43.3kV
Due to strong bunching in steady state some electrons start to hit the the walls and the voltmeter inside the penultimate cavity
Voltage read-out is affected by this problem
Focusing field is now a uniform B field in z direction equal to 3 times the Brillouin field. It has probably to be increased.
Chiara Marrelli

22. GdfidL PIC simulations
Beam current
Convection current in cavity 2
First harmonic to DC current ratio:
GdfidL:
I1 /I0 =0.11
From AJDisk:
I1 /I0 = 0.1
Convection current in cavity 4
First harmonic to DC current ratio:
GdfidL:
I1 /I0 =1.19
From AJDisk:
I1 /I0 = 1.09
Chiara Marrelli

23. GdfidL PIC simulations
Convection current in cavity 5
First harmonic to DC current ratio:
GdfidL:
I1 /I0 =1.07
From AJDisk:
I1 /I0 = 1.36
Convection current at location of output cavity
First harmonic to DC current ratio:
GdfidL:
I1 /I0 =1.3
From AJDisk:
I1 /I0 = 1.6
Chiara Marrelli

24. The Klystron global efficiency depends on the output cavity efficiency
Electrons have to slow down (ideally) until they give all their kinetic energy to the RF field
Main issues:
The beam slows down while energy is removed from it, so we have to be sure that particles do not slip on the accelerating crest of the field (taking energy from the field);
We need to match beam speed and phase velocity multicell structure
Electrons are not relativistic
Space charge forces become dominant at very low beta
We are limited by the speed of slowest electrons (to avoid reflected electrons)
Study of a traveling wave cavity in progress
Chiara Marrelli

25. Output cavity Design method: Gradient along the structure (V/m) (1)
Approximations:
steady state regime
single particle model
no space charge
in this kind of model beam current is assumed constant along the structure
Gradient along the structure (V/m)
[*]
(1)
With:
Where:
ρ = R/Q per unit length
I = first harmonic current
[*] A. Lunin, V. Yakovlev, A. Grudiev, “Analytical solutions for transient and steady state beam loading in arbitrary traveling wave accelerating structures”, PRST-AB 14 (2011)
Chiara Marrelli

26. Output cavity
In case of slow arbitrary variations of vg and ρ along the structure (Q constant)
Slow variations behavior close to a polynomial of degree 3
Gradient (1) can be written as:
(**)
(2)
[**] G. Guignard, J. Hagel, “Closed analytical expression for the electric field profile in a loaded rf structure with arbitrary varying vg and R’/Q”, PRST-AB 3 (2000)
Chiara Marrelli

27. Output cavity Phase advance: h/L=0.18 constant for all cells
Initial cell lengths are set by assuming uniform deceleration of the beam down to ~0.3 βin
we choose initial and final group velocity and assume linear variation along the structure (F1(z))
this sets iris radius a and ρ (F2(z)) for all cells (from 3D plots of ρ(a, L) and vg(a, L) obtained with HFSS simulations)
equations of motion are integrated with gradient (2)
we get β(z), adjust group velocity and cell length to have correct deceleration and phase advance and iterate a
h/2 L b
Chiara Marrelli

28. Output cavity
Preliminary design (5 cells – total length (cm) =18.48 ):
Cell lengths (cm): (5.39, 4.75, 3.67, 2.67, 2.0)
Cell Irises (cm): (0.0263,0.0260, , , )
Group velocity
Gradient
Final beta = 0.18 ~ 0.33 βin
Particles Beta
R/Q per unit length
Chiara Marrelli

29. Thank you for your attention!
Conclusions
The setup of the klystron simulation with GdfidL is now completed and it starts to give good agreement with 1D code;
Beam bunching at the output cavity has to be checked once the beam focusing field will be increased;
A preliminary design of the output cavity is ready and will be tested with PIC code after the design of the coupler.
Thanks to:
Warner Bruns
Alessandro D’Elia
Alexej Grudiev
Aaron Jensen
Erk Jensen
Rolf Wegner
Thank you for your attention!
Chiara Marrelli