Preliminary Modeling of the Breakdown Phenomenon in the AWA Structures

Zikri Yusof, Sergey Antipov, and Wanming LiuArgonne National Laboratory, Argonne, Illinois, USA

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Disclaimer

Still a work in progress; Some of the ideas and models may not be fully baked; There are many different scenarios that have been proposed as the

cause leading to vacuum breakdown. We are focusing only on one narrow possibility.

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Motivation

Understand the breakdown phenomenon (P. Wilson, L. Laurent, G. Nusinovich, …. )

Verify that our model that is consistent with those already established by CLIC and SLAC (example: A. Grudiev and W. Wuensch, 2008 High Gradient Workshop)

Apply specific parameters to the AWA structures Extract the time-dependence temperature evolution in an RF field leading

to possible melting/breakdown Possible testing at a photoinjector dedicated to studying breakdown

phenomenon Solicit from the high-gradient community on possible relevant experiments

and models.

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Motivation for Studying the Time Dependence Temperature Evolution

“It is presently supposed that the ring and tilt, and the electrical breakdown which they precede, were initiated by thermal effects accompanying that temperature increase. It follows from resistive mechanism that the emitter temperature increases with time during microsecond intervals of operation and from the theory of Guth and Mulling that such a temperature increse would cause a corresponding increase of current density with time.” – Dyke et al. PR 91, 1043 (1953).

H.H. Baun et al., CERN/PS 2001-08 (AE)

With the AWA RF parameters and structures, can we possibly detect a time evolution of a temperature increase? More specifically, can we detect this with what we currently have at the AWA breakdown photoinjector?

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Dedicated Photoinjector at the AWA to Study Breakdown Phenomenon

½ cell gun at 1.3 GHz (Q0 = 14000, QL = 5570);

Maximum gradient of 120 MV/m; Crosses and windows available for gated cameras, Faraday cup, etc.; Ability to measure local field-enhancement factor using the Schottky-

enabled photoemission method; Able to use IR laser to heat localized spot on photocathode.

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Modeling of the Temperature Evolution With Time of a Protrusion in an RF Field – Assumptions and Simplifications

We consider only 2 sources of heat: (i) field-emission current (Fowler-Nordheim) through an effective area at the tip of the protrusion, and (ii) Ohmic currents due to the oscillating E-field;

We consider heat loss only due to thermal conduction of copper; We assume that the heat is generated within a finite volume at the tip,

with the effective area as the lower geometrical boundary; We consider only the presence of an oscillating E-field perpendicular to

the bulk surface; Bulk surface material is kept at 300 K; No filling time; Temperature-independent resistivity

Cross section is theeffective area

Heat generated inthis volume

Cu

Cu

Bulk surface

T = 300K

OscillatingE-field

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Determination of Field-Enhancement Factor

min

max

2 micron

10 m

icro

n

Applied gradient, E

Electric field

Col

or -

|E|

= β = 40Enhanced field, Emax

Field-enhancement factor was determined numerically using FEMLAB

Gonzalo Arnau Izquierdo (CERN),2008 CLIC Breakdown Workshop

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Temperature Evolution with Field Emission Current Only

0 5 10 15 20 25 30290

300

310

320

330

340

350

360

T (

K)

Time (ns)

E0 = 100 MV/m

0 5 10 15 20 25 30

500

1000

1500

2000

T (

K)

Time (ns)

E0 = 125 MV/m

0 5 10 15 20 25 30

5000

10000

15000

20000

25000

T (

K)

Time (ns)

E0 = 150 MV/m

0 5 10 15 20 25 30

300

350

400

450

500

550

T (

K)

Time (ns)

125

0 5 10 15 20 25 30

1000

2000

3000

4000

T (

K)

Time (ns)

150

0 5 10 15 20 25 30

296

297

298

299

300

301

302

T (

K)

Time (ns)

100

= 114 at Various E0

E0 = 100 MV/m, Various

= 100 = 125 = 150

E = E0 sin(t)

Cu melting temperature = 1358 K

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Temperature Evolution with Field Emission Current and Ohmic Heating

0 5 10 15 20 25 30

400

600

800

1000

1200

T (

K)

Time (ns)

= 40

E0 = 140 MV/m

E0 = 120 MV/m

E0 = 100 MV/m

• At low gradients, temperature increase is dominated by Ohmic heating;

• At high gradients, temperature increase in dominated by field-emission current;

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Summary

If vacuum breakdown is triggered by melting of the protrusions, then the result of heating due to both field-emission current and Ohmic heating can trigger such an event;

High gradient or high field enhancement factor can cause faster rate of heating;

The results are consistent with the observation that higher gradients can be achieved with shorter pulse length before breakdown occurs or with fewer rate of breakdown;

For low field-enhancement () values (<50) and low gradients, the simple model does not reach the melting point of copper within 30 ns.

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Further Studies

Include temperature dependence behavior of thermal and electrical resistivities. This may change how quickly the temperature builds up;

Consider the possibility of a greater influence of Ohmic heating via the oscillating magnetic fields;

Add filling time; Commission breakdown gun; Consider a possible experiment to monitor the temperature increase on

breakdown gun’s photocathode within a RF pulse.

Acknowledgements

Funding from the US Dept. of Energy Valuable discussion with Kevin Jensen, NRL