# Presentation: 325969

## Preliminary Modeling of the Breakdown Phenomenon in the AWA Structures

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

## 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.

## 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.

## 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?

## Dedicated Photoinjector at the AWA to Study Breakdown Phenomenon

- 1⁄2 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.

## 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 the
- effective area

- Heat generated in
- this volume

**Cu**

**Cu**

- Bulk surface

- T = 300K

- Oscillating
- E-field

## Determination of Field-Enhancement Factor

- min

- max

- 2 micron

- 10 micron

- Applied gradient, E

- Electric field

- Color - |E|

- = *β* = 40

- Enhanced field, Emax

- Field-enhancement factor was determined numerically using FEMLAB

- Gonzalo Arnau Izquierdo (*CERN*),
- 2008 CLIC Breakdown Workshop

## Temperature Evolution with Field Emission Current Only

** = 114 at Various *E**0*

*E**0* = 100 MV/m, Various **

** = 100

** = 125

** = 150

*E* = *E**0* sin(***t*)

- Cu melting temperature = 1358 K

## Temperature Evolution with Field Emission Current and Ohmic Heating

** = 40

***E******0***** = 140 MV/m**

***E******0***** = 120 MV/m**

***E******0***** = 100 MV/m**

- At low gradients, temperature increase is dominated by Ohmic heating;
- At high gradients, temperature increase in dominated by field-emission current;

## 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.

## 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