Potential Designs of High Power Degenerate Band Edge Oscillator (DBEO) for Hot Test at UNM and MIT

Mohamed Othman1, Alex Figotin2 , Filippo Capolino1

1March 03, 2017

1Department of Electrical Engineering and Computer Science, UCI

2Department of Mathematics, UCI

MURI Teleconference, March 2017

I. Degenerate band edge (DBE) in slow-wave structures (SWSs)

II. Degenerate band edge oscillator (DBEO)

III. A number of potential designs for experimental hot test

- Design 1. High power DBEO, compatible with UNM setup

• 12 ns e-beam pulse, ~160 MW pulsed output power

- Design 2. High power DBEO, compatible with MIT setup

• Long e-beam pulse, ~20 MW output power

IV. Conclusion

Outline

2

Degenerate band edge (DBE)

Waveguide structures can support a DBE, instead of only an RBE (regular

band edge). At DBE, we have four degenerate modes

4

DBE dispersion d dk k Periodic slow wave structure (SWS)

j t jkze e

z

Bloch waves

Angula

r F

requen

cy

d

/ d

Figotin, Vitebskiy, Phys. Rev. E, vol. 72,

no. 3, p. 036619, Sep. 2005.

Othman, Capolino, IEEE Microw. Wirel.

Compon. Lett., vol. 25, no. 11, 2015

Evan

esce

nt

d

3

First experimental demonstration of DBE

Othman, Pan, Atmatzakis, Christodoulou, Capolino, (under review), arxiv preprint, arXiv: 1611.03450 (2016) [Link]

Good agreement between full-

wave simulations (CST) and

measurements

Giant scaling of the group delay. The Q factor is proportional to the group

delay : ~Q

Degenerate band edge

Elliptical rings

Degenerate band edge

4

Four mode synchronous operation

4

0 0

2( , , )d d C ku k Ih k k

Dispersion relation for SWS with DBE and e-beam

0d

d

uk

Othman, Veysi, Figotin, Capolino, Phys. Plasmas, Vol. 23, No. 3,

033112, 2016.

Othman, Tamma, Capolino, IEEE Trans. Plasma Sci, Vol. 44,

No. 4, 2016.

Othman, Tamma, Capolino, IEEE Trans. Plasma Sci, Vol. 44,

No. 6, 2016.

0 : electron's average

velocity

u

Angu

lar

Fre

qu

ency d

/ d

Ev

anes

cen

t

Four EM modes e-beam coupling

Leads to enhanced power

transfer between the e-beam

and the DBE modes

Four mode synchronous interaction

5

Periodic slow wave structure (SWS)

d

e-beam

z

Degenerate Band Edge Oscillator (DBEO)

The starting oscillation current

Ist decreases with increasing

DBEO length, as

5, : number of unit cellsstI N

N

DBEO

Othman, Veysi, Figotin, Capolino, IEEE Trans Plasma

Sci, vol 44, no. 6, 918-929, 2016.

Although DBE (cold structure) has

zero group velocity, interaction with

beam dramatically decreases the group delay

- What is left from the DBE is

the four mode interaction

- Starting oscillation time reduces

significantly by increasing the

beam current

DB

EO

sta

rtin

g

tim

e [n

s]

6

Two designs of DBEO for hot test

Design 1. High pulsed power, fast rise time

DBEO compatible with UNM setup with a

short e-beam pulse

Design 2. High power, high efficiency DBEO

compatible with MIT setup with a long e-beam

pulse

Parameter Values Parameter Values

Beam current ~5 kA annular beam Beam current ~80 A solid beam

Beam voltage 500 kV Beam voltage 490 kV

Cathode radius 10 mm Cathode radius 2 mm

Magnetic field 1.5 T Magnetic field 0.15 T

e-beam pulse width ~12 ns e-beam pulse width >1 μs

Rise time 10 ns Rise time 75 ns

Output power > 120 MW Output power ~20 MW

SWS length 290 mm SWS length 350 mm

SWS radius 25 mm SWS radius 35 mm

Output waveguide Horn antenna Output waveguide 2×WR284 waveguides

Frequency ~3.8 GHz Frequency ~3.8 GHz

7

SWS with DBE and strong axial field

‒ A unit cell consisting of circular waveguide loaded with two irises

‒ The iris is formed by two complementary split rings

‒ There is misalignment angle between the split rings

• DBE frequency ~ 3.8 GHz

• Mode distribution has a strong Ez component synchronous to the e-beam

PIC simulations are done using CST Particle Studio 2016

y

z

Ez

8

Dispersion of the DBE mode for various

misalignment angles

1. Plan for hot test at UNM

UNM parameter

setupValue

Beam current Up to 6 kA

Beam voltage Up to 600 kV

Cathode outer

radius10 mm annular

Magnetic field Up to 1.5 T

Beam pulse 12 ns

Maximum SWS

length350 mm (9 solenoids)

Maximum radius 25 mm max

Output waveguideHorn antenna and

windowe-

bea

m p

uls

e sh

ape

Benford, Swegle, Schamiloglu, High power microwaves,

CRC Press, 2015

Photo courtesy of

UNM

E. Schamiloglu,

S. Yurt

UNM set up

‒ All critical parameters are

accommodated in our design

9

Optimized DBEO for UNM experimental setup

TM mode

SWS length 290 mm

Total length

including horn450 mm

horn radius 75 mm

Waveguide

radius25 mm

Magnetic field Up to 1.5 T

Beam voltage 500 kV

Beam current Up to 5 kA

Window (output port)

Circular horn

290 mm

cathode

150 mm

450 mm

50 mm

Simulation parameters

N =16 unit cells240 mm

10

PIC simulation resultse-

bea

m p

uls

e sh

ape

Round trip time ~ 3 ns

UNM SINUS-6 e-beam pulse

Round trip RF signal path

e-

Outp

ut

RF

pow

er [

MW

]

11

e-b

eam

cu

rren

t [A

]

Tunability of the DBEO

A coaxial extraction scheme may

be used to aid the extraction of

power (similar to UNM* design)

Misalignment angle between rings can

be used to tune the output power

• During cold test we will show the tunability of the response

Tunability range of output

power

Beam collection tube

*Kevin Shipman, Experimental Plan for Testing the UNM Metamaterial Slow Wave Structure for High Power Microwave Generation, MURI Teleseminar August 5, 2016.

12

Beam tunnel

Distribution of Ez in the DBEO

Field profile shows some hot spots

of fields between the rings‒ Breakdown investigating (in

progress)

Output radiation pattern‒ Horn antenna design slightly

improves power extraction

Particle energies at t = 8 ns

Distribution of Ez in the DBEO

Aperture field distribution

Field hot spot 13

No

rmal

ized

Ou

tpu

t

spec

tru

m

DBEO design summary

UNM requirement

checkParameter

Values used in UCI

PIC simulations

Pass (current can be

adjusted)Beam current 5 kA

Pass Beam voltage 500 kV

Pass Cathode radius 10 mm

Pass (goes up to 1.6 T

or a bit higher)Magnetic field 1.5 T

Pass (can be

shortened)Rise time 10 ns

Pass (maximum has to

be less that the

9 solenoid lengths)

SWS length 290 mm

PassTotal length

including horn450 mm

Pass (needs

characterization)horn radius 75 mm

Pass (very critical for

solenoid)

Waveguide

radius25 mm

Depending on

measurement setupFrequency 3.8 GHz

RF transient signal

Peak output RF power up to 160 MW after 11 ns

Peak power efficiency ~ 15.5%

Frequency ~3.8 GHz

RF signal spectrum

14

Fabrication and test at UNM

Target

1. Cold test. S-parameters. Dispersion synthesis.

2. Hot test: Optimum number of cells and antenna fabrication

Beam diagnostics (Rogowski Coil)

Frequency diagnostics (waveguide detector)

Power diagnostics (calorimeter)

Output radiation pattern diagnostics (grid)

Breakdown test (PMT)

RF radiation

15

2. Plan for hot test at MIT

• Our DBEO is redesigned to be compatible with MIT setup,

dimensions and beam parameters

• Can also be adapted in rectangular waveguide geometry

Photo taken from MIT teleseminar talks

courtesy of MIT

Hummelt et al, “Design and Test of a

Metamaterial Based High Power Microwave

Generator” MURI teleseminar, MIT, March

2016

Lu et al, “Stage II of Metamaterial Based

Backward Wave Oscillator Experiment at

MIT”, MURI teleseminar, MIT, Sep. 2016

E-beame-beam

WR284 waveguidesMIT Parameter Values

Beam current 84 A solid beam

Beam voltage 490 kV

Cathode radius 2 mm

Magnetic field Up to 0.15 T

Max. SWS length 357.6 mm

Output

waveguide

2×WR284

waveguides

Frequency 2~4 GHz

MIT set up

16

Optimized DBEO for MIT experimental setup

Beam current 80 DC

Beam voltage 490 kV

Cathode radius 2 mm

Magnetic field 0.15 T

Rise time <500 ns17

Port 2 Port 1

Simulation parameters

Output signal in the fundamental TE10 mode

Dimensions

fits MIT

vacuum

setup

Port

2

Distribution of Ez in the DBEO

Field hot spots

TE10 mode

Evolution of Ez field in the DBOE in time

18

Magnetic field variation

Target design

19

from

po

rt1

Magnetic field variation

TE10 mode dominates output power for magnetic field higher than 700 G

Target design

swirling of trajectories occur for Bz<0.07 T

Electron’s trajectories and energies

from

po

rt1

20

PIC simulation summary

Peak power efficiency Psat / (V0I0) ~ 50%

Output RF power ~ 20 MW after 120 ns

Frequency: 3.8 GHz

MIT requirement

checkParameter

Values used in UCI

PIC simulations

Pass (can be

adjusted)Beam current 80 A solid beam

pass Beam voltage 490 kV

pass Cathode radius 2 mm

Pass (can be

lowered)Magnetic field 0.15 T

pass Rise time 75 ns

passMaximum SWS

length357.6 mm

pass Maximum radius 148.3 mm

pass Output waveguide WR284

Pass Frequency 3.8 GHz

Fast rise time

cathodeOutput ports WR284 waveguides

350 mm

70 mm

148 mm

Beam outputtunnel

Port

1P

ort

2

Port 1Port 2

Time [ns]

Outp

ut

pow

er [

MW

]

3.8 GHz

21

Fabrication and hot test at MIT

1. Cold test. S-parameters. Dispersion synthesis.

2. Hot test: Optimum number of cells and antenna

fabrication

Beam diagnostics

Frequency diagnostics (filters to measure power)

Power diagnostics (waveguide attenuator/detector)

Breakdown test

Photo taken from MIT teleseminar talks

courtesy of MIT

Hummelt et al, “Design and Test of a

Metamaterial Based High Power Microwave

Generator” MURI teleseminar, MIT, March

2016

MIT V/I curve at the collector

22

Conclusion

• Degenerate band edge oscillator (DBEO) theory based on four mode

interaction with an e-beam was employed to design efficient high power

microwaves sources

• PIC simulations of metallic SWS with DBE show strong e-beam and EM waves

interaction. High efficiency oscillations are reported

• DBE is found in many SWS geometries, and other special points in the dispersion

can also be engineered and utilized for oscillator and amplifier design

• Both UNM and MIT hot test considerations are accounted for: all the data and

parameters are designed to be compatible with the respective experimental setup

- Design 1. Short pulse-beam, output power 160 MW → UNM setup

- Design 2. Long pulse e-beam, output power 20 MW → MIT setup

• Future work: - Finalize designs, investigate tolerances

- Cold test of the DBE waveguide

- Output extraction optimization. 23

Thank you

24

Auxiliary slides

25

Interaction impedance

Interaction impedance

2

22Re( )

zp

p

zp r

EZ

k P

: component of the Floquet harmonic of the mode

: Bloch wavenumber, : Floquet harmonic

: Power flow

zp

zp

r

E z

k p

P

Fundamental harmonic, p = 0

p = 1

p = +1

Four harmonics of propagating modes

are engaged at the DBE

x

y

z

DBE frequency26