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Preliminary Modeling of the Breakdown Phenomenon in the AWA Structures

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;

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Preliminary Modeling of the Breakdown Phenomenon in the AWA Structures

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  1. Preliminary Modeling of the Breakdown Phenomenon in the AWA Structures Zikri Yusof, Sergey Antipov, and Wanming Liu Argonne National Laboratory, Argonne, Illinois, USA

  2. 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.

  3. 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.

  4. 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?

  5. 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.

  6. 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 Heat generated in this volume Oscillating E-field Cross section is the effective area Bulk surface Cu Cu T = 300K

  7. Determination of Field-Enhancement Factor max Field-enhancement factor was determined numerically using FEMLAB Color - |E| Enhanced field, Emax = β = 40 Applied gradient, E Electric field min 10 micron Gonzalo Arnau Izquierdo (CERN), 2008 CLIC Breakdown Workshop 2 micron

  8. Temperature Evolution with Field Emission Current Only b = 114 at Various E0 E0 = 100 MV/m, Various b b = 100 b = 125 b = 150 E = E0 sin(wt) Cu melting temperature = 1358 K

  9. Temperature Evolution with Field Emission Current and Ohmic Heating b = 40 • At low gradients, temperature increase is dominated by Ohmic heating; • At high gradients, temperature increase in dominated by field-emission current; E0 = 140 MV/m E0 = 120 MV/m E0 = 100 MV/m

  10. 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 (b) values (<50) and low gradients, the simple model does not reach the melting point of copper within 30 ns.

  11. 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

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