Basic of muon ionization cooling K. Yonehara 8/29/11HPRF cavity physics seminar - I, K. Yonehara1

Cool down beam phase space Reduce momentum deviation in beam It is the same mean as increasing density of beam phase space In general, cooling operator is not conserved with Hamiltonian Liuville’s theorem does not hold in cooling except for stochastic cooling 8/29/11HPRF cavity physics seminar - I, K. Yonehara2

Why ionization cooling? Two major cooling methods – Stochastic cooling Pickup deviation of single particle from reference phase space and kick the particle into proper phase space – Electron cooling Transfer beam temperature to cold electron cloud via Coulomb interaction Both cooling methods take a longer time than muon lifetime! – Although there may be some extra space we can improve them to apply for muon beam (e.g. optical stochastic cooling, etc) Ionization cooling – Faster than muon lifetime 8/29/11HPRF cavity physics seminar - I, K. Yonehara3

Note: formula in ionization cooling K 2 is a focusing index Definition of normalized emittance Derivative of normalized emittance w.r.t. z Equilibrium transverse emittance in ionization cooling channel 8/29/11HPRF cavity physics seminar - I, K. Yonehara4

Ionization cooling channel HPRF cavity physics seminar - I, K. Yonehara Perpendicular momentum before cooling absorber Perpendicular momentum after cooling absorber becomes smaller due to ionization energy loss process μ beam Absorber RF cavity Magnet After π → μ decay & μ collection Longitudinal momentum is regained by RF cavity RF cavity is embedded in strong B field (> 2 T) Beam envelop Achievable smallest transverse beam phase space is determined by focus strength (β ⊥ ) and Z & A of cooling absorber 8/29/115

Best cooling material 8/29/11HPRF cavity physics seminar - I, K. Yonehara6

Energy loss & stochastic process Bethe-Bloch formula Maximum transfer energy into electron Mutiple scattering (stochastic in transverse phase space) Scattered off from nucleus Energy straggling (stochastic in longitudinal phase space) Statistic effect; distribution change from Poisson to Gaussian Ref: PDG, Jackson 8/29/11HPRF cavity physics seminar - I, K. Yonehara7

Problem: B field effect on RF cavity HPRF cavity physics seminar - I, K. Yonehara Gradient in MV/m Peak Magnetic Field in T at the Window >2X required field X A. Bross, MC’11 Required E in cooling channel Data were taken in an 805 MHz vacuum pillbox cavity 8/29/118

Illustrated “Standard model” of RF breakdown event HPRF cavity physics seminar - I, K. Yonehara 1. An “asperity” emits a surface electron RF cavity wall 2. Electron gains kinetic energy from E RF cavity wall 3. High energy e - smashes on cavity wall and generates secondary e - 4. Electron heats up cavity wall 5. Repeat heating and cooling wall material induces wall damage Show just dominant process 6. Some amount of wall material is taken off from wall and generates dense plasma near surface B field confines an electron beam and enhances breakdown process as shown in slide 3 8/29/119

Probability of field emission electron (Fowler-Nordheim formula) Hemisphere electrodeBreakdown remnant Breakdown probability as a function of Zenith angle Basically, it comes from tunneling effect A FN = eVA/(MV) 2 B FN = 6830 MV/m (eV) 3/2 β Enhancement factor φ Work function E surf Surface electric field M. BastaniNejad et al, PAC07, WEPMS071 8/29/11HPRF cavity physics seminar - I, K. Yonehara10

Material search High work function & low Z element can be a good material for cooling channel –Beryllium & Aluminum are good candidate HPRF cavity physics seminar - I, K. Yonehara M. Zisman, Nufact’10 Beryllium button assembled 805 MHz pillbox cavity Simulated max grad in an 805 MHz RF cavity with Be, Al, and Cu electrodes Test will be happened in this summer & fall 8/29/1111

RF R&D – 201 MHz Cavity Test Treating NCRF cavities with SCRF processes  The 201 MHz Cavity – 21 MV/m Gradient Achieved (Design – 16MV/m)  Treated at TNJLAB with SCRF processes – Did Not Condition  But exhibited Gradient fall-off with applied B HPRF cavity physics seminar - I, K. Yonehara 1.4m A. Bross, MC’11 8/29/1112

Fill up dense gas to slow down dark current HPRF cavity physics seminar - I, K. Yonehara Maximum electric field in HPRF cavity Schematic view of HPRF cavity 805 MHz High Pressure RF (HPRF) cavity has been successfully operated in strong magnetic fields Metallic breakdown Gas breakdown: Linear dependence Governed by electron mean free path Metallic breakdown: (Almost) constant Depend on electrode material No detail study have been made yet Gas breakdown Operation range (10 to 30 MV/m) P. Hanlet et al., Proceedings of EPAC’06, TUPCH147 8/29/1113

Study interaction of intense beam with dense H2 in high gradient RF field Beam signal (7.5 μs) RF power is lost due to plasma loading RF power is recovered when beam is off RF pulse length (80 μs) p + H 2 → p + H e - Ionization process 1,800 e - are generated by incident K = 400 MeV Huge RF power lost due to electrons’ power consumption But, it is not a breakdown!! ν= 802 MHz Gas pressure = 950 psi Beam intensity = /bunch 8/29/11HPRF cavity physics seminar - I, K. Yonehara Plasma loading in pure H2 gas Equilibrium condition Electron production rate = Recombination rate 14

Preliminary estimation of plasma loading effect in HPRF cavity for cooling channel HPRF cavity physics seminar - I, K. Yonehara From RF amplitude reduction rate, RF power consumption by plasma can be estimated E = 20 MV/m Hence, energy consumption by one electron is (including with initial beam intensity change) Joule t = 200 ns Muon collider: n e per one bunch train = μ × 10 3 e = electrons → 0.6 Joule Neutrino Factory: n e per one bunch train = μ × 10 3 e = electrons → 0.06 Joule A 201 MHz pillbox cavity stores 8.5 Joule of RF power > For MC, 0.6/8.5 of RF power reduction corresponds to 4 % of RF voltage reduction > For NF, 0.06/8.5 of RF power reduction is negligible Plasma loading effect in higher frequency pillbox RF cavity will be severe since the cavity stores less RF power > Need some technique to reduce plasma loading effect ν= 802 MHz Gas pressure = 950 psi Beam intensity = /bunch 8/29/1115

Study electronegative gas effect H2+SF6 (0.01%) gas SF6 removes a residual electron Great improvement! Beam signal (7.5 μs) ν= 802 MHz H2 + SF6 (0.01 % condensation) Gas pressure = 950 psi Beam intensity = /bunch RF pickup voltage 8/29/11HPRF cavity physics seminar - I, K. Yonehara16