Estimate store energy and power dissipation in a simple DL pillbox cell K. Yonehara APC, Fermilab 11/5/14HPRF/RF breakdown meeting, K. Yonehara1

Goal Make a hands-on code to estimate basic RF parameters including with a stored energy and a power dissipation of a simple pillbox cavity with a dielectric material The test geometry is not practical for the engineering design! – There is a high E at the triple junction in the simple test geometry – It generally enhance the breakdown probability However, it should provide us some idea of what is the required RF power source, what is the required cooling power, etc 11/5/14HPRF/RF breakdown meeting, K. Yonehara2

Formulae Conductor part Loaded material part 11/5/14HPRF/RF breakdown meeting, K. Yonehara3

Test geometry a L a1a1 a2a2 Recent measurement 11/5/14HPRF/RF breakdown meeting, K. Yonehara4      

Analytic field expression in DL cavity 11/5/14HPRF/RF breakdown meeting, K. Yonehara5 General solution of Ez in axial symmetric condition J 0 (k c x) Y 0 (k c x) Because Y 0 (0) is infinite, hence c 2 = 0 at r = 0. Boundary condition: E z = E z,0 at r =0 → c 1 = E z,0 E z (a 1 ) = E z ’(a 1 ) & ∂ r E z (a 1 ) = ∂ r E z ’(a 1 ) E z ’ = 0 at r =a Solve the equation to extract c 3, c 4, k c =  c /v or a

Example result Pillbox + completely fill with DM Pillbox + partially fill with DM a = m Q = 7,518 U = 2.34 J P = 1.27 MW a = m Q = 2,158 U = 1.17 J P = 2.21 MW a = m Q = 4,656 U = 4.95 J P = 4.34 MW 11/5/14HPRF/RF breakdown meeting, K. Yonehara6 Ez r HH Similar as a reentrant cavity Ez HH

Verification of my calculation Superfish calculation by Mike Neabauer 325 MHz DL RF 11/5/14HPRF/RF breakdown meeting, K. Yonehara7

SF vs my calculation Normalized Ez r (m) Blue: Vacuum pillbox Point: SF made by MN Orange: Partially filled with DM 11/5/14HPRF/RF breakdown meeting, K. Yonehara8

Some observations at ver.3 Field calculation is cross-checked with various other codes – See slide 6&7 for verification Re-evaluate Q factor after discussing with Al – See slide 5 Large stored energy in a partial filled cavity What’s next? – Optimize cavity size & operation condition, e.g. cryogenic temperature 11/5/14HPRF/RF breakdown meeting, K. Yonehara9

Optimization 11/5/14HPRF/RF breakdown meeting, K. Yonehara10 Conductance of copper (1/Ohm) Blue:  = 5.8E7 (room temperature) Orange:  = 3.9E8 (80 K) Green: Beam hole radius 5 cm → 3 cm Goal peak power is 1 MW or less. We need to operate the cavity at LN2 temperature. The peak power is ~0.5 MW in a pillbox cavity. Q0 Peak power [MW] Loss tangent