# Presentation: 193753

## Klystrons

- (and other vacuum electronics power amplification devices)
- Gap-Coupling, Beam-Loading Admittance
- Eric Colby,
- SLAC
- USPAS, January 21st

## Outline

-  How a linac’s properties interact with the power source
-  General principles of microwave tubes
- Beam loading admittance
- Radial gap-coupling coefficient
- Bunching
-  Specific examples
-  General scaling laws
-  Other examples

## Linac / Power Source Parameter Couplings

- Linac Gradient 		G’ = sqrt(P’ Z’s T)
- 		G’ = gradient per unit length
- 		P’ = rf peak power per unit length
- 		Z’s=shunt impedance per unit length
- 		T = transit time factor
- Linac fill time 		=QL/2 << rf = rf pulse length
- 		QL =Accelerating loaded cavity QL=Qo/(1+)
- Average Beam Power  	Pb =  Prf
- 		Pb=(average beam current) x (beam voltage gain)
-  = net efficiency of coupling rf to beam
- 		Prf= rf average power (=f*rf*Ppeak)
- Linac coupling factor 	 = VSWR (oc) @ tube
- Phase stability of linac 	phase stability of source
- 				frequency stability of source

## Basic Klystron

- RF power input
- “RF Drive”

- RF power output

- Energy modulation

- D

- Vz,0, I0

- Vz,0, I1

- modulate

- decelerate

- Vc

- Ez

- Ez

- Velocity bunching

- Beamtube must not propagate the rf backward wave or the tube can oscillate!

## Beam Loading Admittance

- So far, we’ve taken 1 in treating beam/cavity interaction, which allows for the approximation of the beam as an ideal current source (i.e. the beam current is **not** modified by the gap voltage in the cavity).
- For vacuum power tubes, however, ~(0.2-0.8)  (V=10kV-500kV), and the beam current changes significantly while *in the gap.*

- 0  DC   1  rf

## Beam Loading Admittance

- Proceeding from the Continuity equation and Lorentz force law, the action of the rf fields on the beam velocity and density can be described, yielding:

- Gap transit angle

## Beam Loading Admittance

- From E. Craig, “The Beam-Loading Admittance of Gridless Klystron Gaps”, IEEE Trans. Elec. Dev. **14** (5), p. 273ff, (1967).

- Gc

- Bc

- Solid – gridless gap
- Dashed – gridded gap

- Normal range

- Gap length L
- Gap transit  angle =L/c

## Gap Coupling

- r

- The beams used in vacuum tubes generally occupy a significant fracation of the beam pipe (often rb =2/3 Rpipe), so the variation of the gap fields with r must be accounted for. This is done with the **radial gap coupling coefficient.**
- The solution to wave equation in cylindrical coordinates yields the form of the gap voltage with r:

- Averaging over the beam’s cross section yields the gap coupling coefficient:

- [R/Q][R/Q]*M2

## Ballistic Bunching

- Ballistic (no space charge) Theory
- Matlab demonstration (space charge free)

- Bunching parameter

- Transit angle of drift D

## Klystron Efficiency vs. Perveance

- k=I/V3/2

## Real Klystron Schematic

- D. Sprehn, R. Phillips, G. Caryotakis, “Performance of a 150-MW S-Band Klystron”, AIP Conf. Proc. 337, p.43ff, (1994).

- Diode

- Drive Cavity

- Idler Cavities

- Output Cavity

- Collector

- Guide-field Solenoid

## DESY S-Band Tube (short-pulse)

- D. Sprehn, R. Phillips, G. Caryotakis, “Performance of a 150-MW S-Band Klystron”, AIP Conf. Proc. 337, p.43ff, (1994).

- f = 2996 MHz		Gain = 55 dB			Efficiency: >40%
- P = 150 MW		B~2100 Gauss			PRF: 60Hz
- K = 1.8 P		Group Delay 150 nsec		Pulse length: 3 s
- Vb = 535 kV		Jcath = 6 A/cm2			Ib= 700 Amps

## B-Factory Tube (CW)

- f = 476 MHz		Gain > 43 dB			Efficiency: >50%
- P = 1.2 MW CW		BW = +/- 3.0 MHz at -1dB points	VSWR tolerance: 1.2
- K = 0.83-1.3		Group Delay 150 nsec
- Vb = 83 kV		Jcath = 0.63 A/cm2			Ib= 24 Amps CW

## Klystron Amplifier Scalings

- Cathode current density:* f **0*

- Focusing field strength: B~***q**-1*

- Output Cavity Gap Fields ~*f **0*

- Circuit losses: *f **1⁄2*

- Beam area convergence: *f **0*

**Beam Power & Output Power: *****f ******-2***

- Tube length: q~V3/2

## Design Issues

- Slide courtesy of J. Hirshfield, to be published in Proc. 10th Adv. Accel. Conc. Workshop, Oxnard, CA, June 23-28 (2002).

## Typical operational problems with a klystron

- Input drive power is too low and klystron is not saturated (although this is *required* if the tube is included in a feedback loop)  reduced output power, efficiency, and increased output power amplitude jitter
- Wrong cathode filament current  wrong perveance  poor efficiency (minor) or beam interception (major)
- Modulator voltage jitter causes jitter in
- The tube output power P~V5/2  P/P~(5/2)(V/V)
- The tube transit time, which in turn causes phase jitter on the output ∂/ ∂V=(Lf/33c)
- Mismatched load causes significant output instability

## Typical Klystron Failure Modes

- Burnt-out or shorted cathode filament
- Beam interception erodes output cavity
- Rf breakdown erodes the output cavity
- Multipactoring on or near the output window sputters metal onto the ceramic window, resulting in breakdowns
- Slow vacuum leak contaminates (“poisons”) the cathode
- Focusing magnetic field changes, resulting in a current density change that either:
- If minor: changes the gap-coupling and space charge forces
- If major: results in beam interception
- Input cavity erodes (rare)
- Output cavity oscillates (not necessarily at an integer multiple of the rf frequency)
- Gun supports an rf resonance

## Examples of other beam-based power amplifiers

## 17.136 GHz Klystron (Haimson Research, NRL)

- Taken from J. Haimson, B. Mecklenberg, B. Danly, “Initial Performance of a High Gain, High Efficiency 17 GHz Traveling Wave Relativictic Klystron for High Gradient Accelerator Research”, in AIP Conf. Proc. 337, p.146ff, (1994).

- 17.136 GHz Klystron (Haimson Research, NRL)

## 17.136 GHz Klystron

- Taken from J. Haimson, B. Mecklenberg, B. Danly, “Initial Performance of a High Gain, High Efficiency 17 GHz Traveling Wave Relativictic Klystron for High Gradient Accelerator Research”, in AIP Conf. Proc. 337, p.146ff, (1994).

- (Haimson Research, NRL)

- Measured Properties:
- Output Power: 26 MW @ 150 ns
- Efficiency: 49%
- Saturated Gain: 67 dB
- 560 kV/95 A beam

## SLAC SBK Work

**1 MW, 91.4 GHz Sheet Beam Klystron (SLAC/MRC)**

## L. Song, et al, in PAC03 proc. 

- L. Song, *et al*, in PAC03 proc.

## The Gyroklystron

- Taken from M. Blank, * et al*, “Experimental Demonstration of High Power Millimeter Wave Gyro-Amplifiers”, AIP Conf. Proc. 474, p. 165ff, (1998).

- Test Load

**Synchronism condition: ********-k****||****z****||****=n********c**

- TE011

## Helix TWT (Preamplifier)

- Generally used for driving klystrons.
- Gain (typ)~20-30 dB
- Output~1 kW or less

## 34 GHz Magnicon(Omega-P)

- Taken from O. Nezhevenko, * et al*, “High Power Pulsed Magnicon at 34-GHz”, AIP Conf. Proc. 474, p. 195ff, (1998).

- Transverse Deflection

- Energy

## Ubitron or Free Electron Laser

- Taken from R. Phillips, “Conceptual Designs for NLC Ubitrons with Permanent-Magnet Wigglers”, AIP Conf. Proc. 317, p.239, (1994).

## LLNL 140 GHz FEL Amplifier

- Taken from S. Allen, *et al*, “Generation of High Power 140 GHz Microwaves with an FEL for the MTX Experiment”, in Proc. IEEE Part. Accel. Conf. (PAC 93), Washington, D.C., p.1551ff, (1993).

- Measured Properties:
- Power: 1-2 GW **(!)**	@ 20 ns
- Efficiency: 14%
- Beam: 6 MV/2500A

## Compact Linear Collider (International collaboration centered at CERN)

- Compact Linear Collider (International collaboration centered at CERN)

## CLIC Test Facility II

- Taken from: H. Braun, *et al*, “Experimental Results and Technical Research and Development at CTF II”, in Proc. Euro. Part. Accel. Conf., Vienna, Austria, p.48ff, (2000).

- CTF-II Demonstrated:
-  Generation and acceleration of 48x13.4 nC drive beam
-  120 MW of 30 GHz power generation in 16 ns pulses from the Power Extraction and Transfer Structures
-  59 MV/m acceleration of the probe beam

- CLIC Test Facility II

- Inset photo taken from H. Braun, *et al*, “A New Method for RF Power Generation for Two-Beam Linear Colliders”, AIP Conf. Proc. 474, p. 1ff (1998).

## High Power Fiber Lasers

- http://www.ipgphotonics.com/documents/documents/HP_Broshure.pdf

## Carrier Phase-Locked Lasers

- Interference fringes of carrier phase-locked white light continua generated from Ti:Sapphire laser.
- M. Bellini, T Hansch, Optics Letters, **25** (14), p.1049, (2000).

## Sources by Power Density and Wavelength

- Source Wavelength

- cm               cm 	          mm 	  	nm

**Notes:**
Simplify: keep to 1-minute summary
Single-frequency vs. broadband source distinction
Coupling in single-frequency structures vs. broadband coupling