Particle-in-Cell Modeling of Rf Breakdown in Accelerating

Structures and Waveguides

Valery Dolgashev,

SLAC National Accelerator Laboratory

Breakdown physics workshop,May 6th-7th, 2010,

CERN

Some of the results were published in

• Valery A. Dolgashev, Sami G. Tantawi, “RF Breakdown in X-band waveguides,” Proceedings of EPAC 2002, Paris, France, pp. 2139-2141

• Valery A. Dolgashev, Sami G. Tantawi, “Simulations of Currents in X-band accelerator structures using 2D and 3D particle-in-cell code,” SLAC-PUB-8866, Proceedings of the 2001 Particle Accelerator Conference, June 18-22, Chicago, Illinois. pp. 3807-3809.

• V.A. Dolgashev, T.O. Raubenheimer, “Simulation of RF Breakdown Effects on NLC Beam,” SLAC-PUB-10668, Proceedings of LINAC 2004, Lübeck, Germany.

• Karl L. F. Bane, Valery A. Dolgashev, Tor Raubenheimer, Gennady V. Stupakov, and Juhao Wu, “Dark currents and their effect on the primary beam in an X-band linac,” Phys. Rev. ST Accel. Beams 8, 064401 (2005) [11 pages]

Outline• Properties of rf breakdown in waveguides and

traveling wave (TW) accelerating structures• PIC model, based on “cathode spot”• Waveguides• Traveling Wave structures

– Ion current dependence– Beam pipe current mystery– Absorbed power

• Beam kick due to RF breakdown in TW structure

Properties of RF Breakdown in

Waveguides and Traveling Wave

Structures

Geometries

Low magnetic field waveguide, height 10 mm High magnetic field waveguide, height 1.3 mm

• The peak electric field surface area equal that of the low magnetic field waveguide

• For a given input power both waveguide have the same peak electric field — 80 MV/m at 100 MW of rf power

• Ratio between magnetic field at peak field between both guides = 21

Sami Tantawi

Electric field Magnetic field

Low magnetic field waveguide

High magnetic field waveguide

Field Distribution

Sami Tantawi

-750 -500 -250 0 250 500 750 1000

Time [ns]

20

40

60

80

100

120r

ew

oP

W]

[M34

Incident

Transmitted

Reflected

RF signals of breakdown

Breakdown event in waveguide, absorbed 30% energy and up to 80% power

~40 ns

Sami Tantawi

900 1000 1100 1200 1300 14000

20

40

60

900 1000 1100 1200 1300 14000

5

10

15

20

25

Measurements of a Breakdown event in TW structure, up to 80% power absorbed

RF breakdown in TW structure

Reflected Pulse

Transmitted Pulse

Time (ns)

Pow

er (

MW

)Po

wer

(M

W)

Chris Adolphsen

• Complete shut-off of transmitted power• Time constant of the power shut-off 20-200ns• Absorbed power 0-80% • Spectral lines of the light are mostly from neutral

copper atoms (waveguide breakdown)

Main Features of RF breakdown in TW structures and waveguides

3D PIC simulation of breakdown in waveguide

1. Model geometry 2. Physical model 3. Space charge limited emission of electrons only4. Space charge limited emission of electrons and copper

ion beam5. Space charge limited emission of electrons, copper ion

beam and neutral gas

3D geometry of the low rf magnetic field waveguide

y-z plane x-z plane

Physical model of breakdown

• Space charge limited emission of electrons• Copper ions • Neutral copper gas

3D PIC simulation of breakdown in waveguide

3D PIC simulation of breakdown in waveguide

Spot size 1.6x1.6mm, space charge limited emission of electrons

Projection of phase space on the x-z plane

Model• Space charge limited emission of electrons

3D PIC simulation of breakdown in waveguide

Spot size 1.6x1.6mm, space charge limited emission of electrons,

average current 40 A

Projection of phase space on the z-γ plane

3D PIC simulation of breakdown in waveguide

0 20 40 60 80 100 1200

50

100

inputreflectedtransmitted

Time [nsec]

Pow

er [

MW

]

Emission spot 4x4 mm, space charge limited emission of electrons, input power 80 MW, breakdown at 2 ns

• In order to significantly disrupt RF power spot size should be > 2cm2

• Fast transient process ~ns• ~50% of emitted current returns back to the emitting spot

Result

3D PIC simulation of breakdown in waveguide

3D PIC simulation of breakdown in waveguide

Model

• Space charge limited emission of electrons• Copper ion beam with current needed to disrupt transmitted

power

Spot size 1.6x1.6mm, copper ion current ~8A

Fast electron motion, projection of phase space on the x-z plane

3D PIC simulation of breakdown in waveguide

Spot size 1.6x1.6mm, copper ion current ~8A

Fast electron motion, projection of phase space on the z-γ plane

3D PIC simulation of breakdown in waveguide

Low magnetic field waveguide, spot size 1.6x1.6mm, copper ion current ~8A

Electron - ion motion, projection of phase space on the x-z plane

3D PIC simulation of breakdown in waveguide

High rf magnetic field waveguide, spot size 0.6x0.6mm, copper ion current ~35A

Spot size 1.6x1.6mm, copper ion current ~8A

Slow ion motion, projection of phase space on the z-γ plane

3D PIC simulation of breakdown in waveguide

0 10 20 30 40 50 60 70 800

50

100

inputreflectedtransmitted

Time [nsec]

Pow

er [

MW

]

Spot size 1.6x1.6mm, copper ion current ~8A

Input, reflected and transmitted power vs. time

3D PIC simulation of breakdown in waveguide

Spot size 1.6x1.6mm, copper ion current ~8A

Emitted electron current vs. time

3D PIC simulation of breakdown in waveguide

Spot size 1.6x1.6mm, copper ion current ~8A

Electron current destroyed at the emission spot

Power of electrons destroyed at the emission

spot

3D PIC simulation of breakdown in waveguide

3D PIC simulation of breakdown in waveguide

0

20

40

60

80

100

120

0 50 100 150 200 250 300 350

inputreflectedtransmitted

time [ns]

0

20

40

60

80

100

120

0 50 100 150 200 250 300 350

inputreflectedtransmitted

time [ns]

Measurements, 24 April 2001,18:13:40, shot 45

3D PIC simulations, 4x4 mm emitting spot, electron current 7kA, copper ion current 30A

V.Dolgashev, S. Tantawi

• Ions cross the waveguide in ~30 ns• Time constant of the power shut-off 10-20 ns• Ion current determines electron current by compensating

space charge of electrons• Oscillation of transmitted and reflected power determined by

ion-electron density ~ 10-40 ns• ~80% of emitted current returns back to the emitting spot• Maximum absorbed power 50%

Result

3D PIC simulation of breakdown in waveguide

Model• Space charge limited emission of electrons• Copper ion beam with current needed to disrupt transmitted

power• Drag associated with presence of neutral copper ions

3D PIC simulation of breakdown in waveguide

• Maximum absorbed power up to 75%• Ion-electron oscillation damped

Result

Transmitted powerInput - reflected power

Higher power absorption

Traveling wave accelerating structures

3D PIC model based on properties of “cathode spot”

• Matched traveling wave structure with coaxial couplers

• Emission of ion beam with predetermined current from small spot on iris

• Space charge limited electron current from the same iris

Ion current dependence

Procedure: Increase ion current until transmitted power completely shuts off

3D PIC simulations, T20VG5, 5 A ion current, cell breakdown, 5 cell structure, spot ~2mm2

V.A.Dolgashev, 6 December 02

3D PIC simulations, T20VG5, 5 A ion current, 5 cell structure, cell breakdown, spot ~2mm2

V.A.Dolgashev, 6 December 02

3D PIC simulations, T20VG5, 5 A ion current, cell breakdown, 5 cell structure, spot ~2mm2

V.A.Dolgashev, 6 December 02

rf Emitted currents

Beam pipe currents Back-bombardment currentsV.A.Dolgashev, 6 December 02

3D PIC simulations, T20VG5, cell breakdown, 5 A ion current, 5 cell structure, spot ~2mm2

0 20 40 60 800

2

4

6

8

ElectronsIons

Time [ns]

Cur

rent

, ion

s [A

], e

lect

rons

[kA

]

0 20 40 60 800

5

10

15

20

ElectronsIons

Time [ns]

Cur

rent

, ion

s [A

], e

lect

rons

[kA

]

0 20 40 60 800

10

20

30

40

50

60

70

80

InputTransmittedReflected

Time [ns]

Pow

er [

MW

]

0 20 40 60 8050

0

50

100

InputOutput

Time [ns]

Cur

rent

, ele

ctro

ns [

A]

3D PIC simulations, T20VG5, coupler breakdown, 10 A ion current, 5 cell structure, spot ~2mm2

V.A.Dolgashev, 6 December 02

3D PIC simulations, T20VG5, coupler breakdown, 10 A ion current, 5 cell structure, spot ~2mm2

V.A.Dolgashev, 6 December 02

rf Emitted currents

Beam pipe currents Back-bombardment currentsV.A.Dolgashev, 6 December 02

3D PIC simulations, T20VG5, coupler breakdown, 10 A ion current, 5 cell structure, spot ~2mm2

0 10 20 30 40 50 600

5

10

15

ElectronsIons

Time [ns]

Cur

rent

, ion

s [A

], e

lect

rons

[kA

]

0 10 20 30 40 50 600

10

20

30

40

50

60

ElectronsIons

Time [ns]

Cur

rent

, ion

s [A

], e

lect

rons

[kA

]

0 10 20 30 40 50 6050

0

50

100

150

InputOutput

Time [ns]

Cur

rent

, ele

ctro

ns [

A]

0 10 20 30 40 50 600

10

20

30

40

50

60

70

80

InputTransmittedReflected

Time [ns]

Pow

er [

MW

]

3D PIC simulations, T20VG5, coupler breakdown, spot ~2mm2 , ion current 20 A

V.A.Dolgashev, 6 December 02

3D PIC simulations, T20VG5, coupler breakdown, spot ~2mm2 , ion current 20A

V.A.Dolgashev, 6 December 02

3D PIC simulations, T20VG5, coupler breakdown, spot ~2mm2 , ion current ~20 A

V.A.Dolgashev, 6 December 02

rf Emitted currents

Beam pipe currents Back-bombardment currentsV.A.Dolgashev, 6 December 02

3D PIC simulations, T20VG5, coupler breakdown, spot ~2mm2 , ion current ~20A

0 10 20 30 40 500

10

20

30

ElectronsIons

Time [ns]

Cur

rent

, ion

s [A

], e

lect

rons

[kA

]

0 10 20 30 40 500

10

20

30

40

50

60

ElectronsIons

Time [ns]

Cur

rent

, ion

s [A

], e

lect

rons

[kA

]

0 10 20 30 40 500

10

20

30

40

50

60

70

80

InputTransmittedReflected

Time [ns]

Pow

er [

MW

]

0 10 20 30 40 50100

0

100

200

InputOutput

Time [ns]

Cur

rent

, ele

ctro

ns [

A]

Mystery of small beam pipe currents:

Beam currents through output pipes during breakdown are

small ~100 mA, while currents in the cell are ~10 kA.

Why output current are only ~0.001% of cell currents?

V.A.Dolgashev, 6 December 02

3D PIC simulations, T20VG5, coupler breakdown, spot ~4mm2

V.A.Dolgashev, 6 December 02

3D PIC simulations, T20VG5, coupler breakdown, spot ~4mm2

rf Emitted currents

Beam pipe currents Back-bombardment currentsV.A.Dolgashev, 6 December 02

0 20 40 60 80 100 1200

10

20

30

ElectronsIons

Time [ns]

Cur

rent

, ion

s [A

], e

lect

rons

[kA

]

0 20 40 60 80 100 1200

10

20

30

40

50

60

ElectronsIons

Time [ns]

Cur

rent

, ion

s [A

], e

lect

rons

[kA

]

0 20 40 60 80 100 1200

10

20

30

40

50

60

70

80

InputTransmittedReflected

Time [ns]

Pow

er [

MW

]

0 20 40 60 80 100 12050

0

50

100

150

InputOutput

Time [ns]

Cur

rent

, ele

ctro

ns [

A]

Beam kick due to rf breakdown

This work we did with Juhao Wu

Breakdown simulation in single-cell TW structure,emission from downstream side of the first iris

(cell breakdown)

Breakdown currents and beam

RF characteristics, cell breakdown

Horizontal kick, cell breakdown, on axis

0 2 4 6 8 10 12 14 16 18 20200

100

0

100

200

phi = 0phi = Piaccleration /10

Time [ns]

Kic

k [k

V]

Horizontal kick, cell breakdown, on axis

11 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9200

100

0

100

200

phi = 0phi = Piaccleration /10

Time [ns]

Kic

k [k

V]

Horizontal kick, coupler breakdown, on axis

0 2 4 6 8 10 12 14 16 18 20200

100

0

100

200

phi = 0phi = Pi

Time [ns]

Kick

[kV

]

Horizontal and vertical kicks, coupler breakdown, on axis

12 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9200

100

0

100

200

phi = 0phi = Piaccleration /10

Time [ns]

Kick

[kV

]

SUMMARY• Model of “plasma spot” with ion current of ~30 A reproduces rf

breakdown signals for “soft event” in waveguide with ~1 cm height.

• Same model with ion current of ~20 A reproduces rf breakdown signals for “soft event”(~25% of input power absorbed in steady-state breakdown) in traveling wave structure

• Breakdown can potentially kick beam ~100 kV transversely, the kick strongly depends on accelerating rf phase

• To explain “hard events” with absorption of more then 25% of input power and extremely small beam pipe currents model need additional assumptions: for example drag and scattering for electrons on neutral copper gas or something else

• This simple model can’t predict power shutoff in narrow (~1mm height) waveguide, need additional assumption about expansion of the ion-emitting spot