Design Considerations for a

Metamaterial Backward-Wave

Oscillator

Jason S. Hummelt

MURI TeleconferenceApril 4th, 2014

Outline Introduction and review: MTMBWO

Experimental Progress Cold Tests

Engineering Considerations

Update on the Experiment

Conclusions

#2

Goals and Update Design and test of S-band Backward Wave Oscillator

Design change from 2.6 GHz to SLAC frequency: 2.856 GHz

MTM interaction circuit

Utilize existing 500 keV, 80 A electron gun Long pulse: 1 μs flat top

Electrostatically focused, space-charge limited

#3

Electron Gun

Magnets

MTM circuit must withstand high

power microwaves Output Power ~ 5 MW

New publication Hummelt, Lewis, Shapiro, and Temkin,

Design of a Metamaterial-Based

Backward-Wave Oscillator, IEEE Trans.

Plasma. Sci.

http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnu

mber=6778078

MTM Design Complementary split-ring resonator (CSRR)

Robust and all-metallic

No lossy dielectrics

#4

Guide is below cutoff (3.98 GHz)

CSRR’s resonance below cutoff

in waveguide

Below cutoff waveguide has

μ < 0, CSRRs provide ε < 0

Structure Electromagnetic Design HFSS eigenmode

simulation Fields, dispersion, beam

coupling

Beam coupling Depends strongly on

MTM plate spacing

#5

Beam line:

Operating point

Positive Index TM-like

Negative Index TM-like

Negative Index

Simulation upper ½ structure (symmetry); 1 period ‘p’

E-Beam2𝜋𝑓 − 𝑘𝑧vbeam=0

Field Profile from HFSS

2.6 GHz

CST PIC Results

#6

Electron beam bunches at λz=9 cm

CST Fields indicate backward

wave, with power going out ports

(back) along MTM plates

t=400 ns

Perspective: fields along midplane

E-beam Direction

t=400 ns

t=400 ns

CST Results: Output Power

#7

Total power out of ports 1 and 2 Includes ohmic (copper structure), coupling losses

Stationary power level: 5.75 MW

FFT of Stationary Output

Turn on Time (260 ns)

Stationary Power (5.75 MW)

Cold Test 1 Design and test of a ‘short’ MTM structure (20

periods): Brass, ‘Side’ Coupling

Floating plates: problem with design Fixed with clamping

#8

CST Sim.

Measured

Cold Test 2 Design and test of a full length MTM

structure (47 periods, 376 mm) Copper

‘Front’ Coupling

Design modified to prevent ‘floating’ MTM

5 dB flaw at 2.7 GHz may be due to

poor contact Silver epoxy (2e5 S/m vs. 5e7 S/m for

copper) rubbed off on copper MTM

Final design: MTM plates sit in ‘pockets’ of

rectangular guide, guide is bolted together

#9

CST Sim

Measured

Breakdown Power Simple estimate from HFSS eigenmode simulation-take peak field and

power flux and scale to breakdown field

SLAC: 11.4 GHz start to see breakdown near 200 MV/m

Conservative estimate: breakdown field in device is 100 MV/m

𝑃𝑏𝑟𝑒𝑎𝑘𝑑𝑜𝑤𝑛 = 16 𝑀𝑊

#10

𝑃 =1

2𝑅𝑒 𝐸 × 𝐻∗ ∙ 𝑑 𝐴

Pulsed Heating Follow method outlined by Pritzkau-PRSTAB 2002

Can estimate pulsed heating by knowing peak H field, 𝐻𝑃𝑒𝑎𝑘, from HFSS simulations

We calculate the peak H field from the HFSS result at a given power as we did the breakdown E field and scale to operating power

Assuming a max of 10 MW of RF power

This temperature rise occurs on surface of metal-bulk temperature rise due to conduction

#11

∆𝑇 =1

𝜌𝑐𝜀 𝜋𝛼𝑑

1

2𝜋𝜇𝑓𝜌𝑟𝑒𝑠𝐻𝑝𝑒𝑎𝑘

2 𝜏

∆𝑇 =19 K

𝜌9000

𝑘𝑔

𝑚3

𝛼𝑑0.00011

𝑚2

𝑠

𝑐𝜀 385𝐽

𝑘𝑔 𝐾

𝜌𝑟𝑒𝑠 1.7 ∗10−8Ω𝑚

𝑓 2.865 𝐺𝐻𝑧

𝜇4𝜋 ∗ 10−7

𝐻

𝑚

𝜏 10−6𝑠

End Reflection

Limited space between magnetic lens and solenoid: reflect backward wave Couple out collector side

Reflection has an effect on device efficiency Can be thought of as a monotron + BWO due to strong end reflection

Original Concept Spatially growing backward wave

Open Boundary

Updated Concept

Metal Reflector

Uniform Field Intensity

#12

Power Characteristics Device performance scanned over length and coupling impedance

Coupling impedance changed by changing d-spacing between MTM plates Impedance calculated for 3 mm radius beam from HFSS eigenmode

#13

White Space: not yet calculated

Design Point

Design Update

Lens

Beam Profile

Magnet System on Aligned Sliding Rails

50 L/s Pump

Solenoid

Vacuum Chamber

MTM Structure

Viewport

CollectorElectric Standoff

Bethe Hole Coupler

RF Load

SLAC type UHV flange

RF Load Pump Port

#14

SLAC RF Components

#15

½ window assembly

SLAC type crush flange-copper gasket provides UHV seal

Bethe hole coupler(~60 dB)

Ceramic brazed over hole

Stripline detector measures power

Conclusions

#16

Observed in simulation self start-up of 2.6 GHz negative index mode HFSS/CST agreement

>5 MW output power

Measured the transmission of two test MTM structures for 2.6 GHz design Good agreement w/ theory

Helped identify potential construction problems in holding MTM plates

Investigated use of reflector to bring power out collector side of experiment Characterized device performance over set range of operating parameters

Designs of MTMBWO experiment near completion Redesigned at 2.856 GHz to match SLAC

Initiated construction phase-MIT machine shop to perform majority of machining

Bids on RF assemblies to outside vendors

Experiments to start Fall, 2014

Acknowledgements MURI collaborators

LSU

UNM

Ohio State

UC-Irvine

SLAC

MIT WAB–staff Rick Temkin

Ivan Mastovsky

Michael Shapiro

Bill Guss

Paul Woskov

Sudheer Jawla

MIT WAB-students Sergey Arsenyev

Elizabeth Kowalski

Samantha Lewis

Xueying Lu

Brian Munroe

Alexander Soane

Sam Schaub

Haoran Xu

JieXi Zhang