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Beam Cooling Beam Cooling M. Steck, GSI, Darmstadt CAS, Warsaw, 27 September – 9 October, 2015 Beam Cooling longitudinal (momentum) cooling injection into the storage ring transverse cooling time Xe54+ 50 MeV/u p/p Xe54+ cooling off 15 MeV/u heating (spread) and cooling: energy loss (shift) good energy definition time small beam size highest precision with internal gas cooling on target operation M. Steck (GSI) CAS 2015, Warsaw Beam Cooling Introduction 1. Electron Cooling 2. Ionization Cooling 3. Laser Cooling 4. Stochastic Cooling M. Steck (GSI) CAS 2015, Warsaw Beam Cooling Beam cooling is synonymous for a reduction of beam temperature. Temperature is equivalent to terms as phase space volume, emittance and momentum spread. Beam Cooling processes are not following Liouville‘s Theorem: `in a system where the particle motion is controlled by external conservative forces the phase space density is conserved´ (This neglects interactions between beam particles.) Beam cooling techniques are non-Liouvillean processes which violate the assumption of a conservative force. e.g. interaction of the beam particles with other particles (electrons, photons, matter) M. Steck (GSI) CAS 2015, Warsaw Cooling Force Generic (simplest case of a) cooling force: vx,y,s velocity in the rest frame of the beam non conservative, cannot be described by a Hamiltonian For a 2D subspace distribution function cooling (damping) rate in a circular accelerator: Transverse (emittance) cooling Longitudinal (momentum spread) cooling M. Steck (GSI) CAS 2015, Warsaw Beam Temperature Where does the beam temperature originate from? The beam particles are generated in a ‘hot’ source at rest (source) at low energy at high energy In a standard accelerator the beam temperature is not reduced (thermal motion is superimposed the average motion after acceleration) but: many processes can heat up the beam e.g. heating by mismatch, space charge, intrabeam scattering, internal targets, residual gas, external noise M. Steck (GSI) CAS 2015, Warsaw Beam Temperature Definition Longitudinal beam temperature Transverse beam temperature Distribution function Particle beams can be anisotropic: e.g. due to laser cooling or the distribution of the electron beam Don‘t confuse: beam energy beam temperature (e.g. a beam of energy 100 GeV can have a temperature of 1 eV) M. Steck (GSI) CAS 2015, Warsaw Benefits of Beam Cooling . Improved beam quality • Precision experiments • Luminosity increase . Compensation of heating • Experiments with internal target • Colliding beams . Intensity increase by accumulation • Weak beams from the source can be enhanced • Secondary beams (antiprotons, rare isotopes) M. Steck (GSI) CAS 2015, Warsaw 1. Electron Cooling ve║ = ec= ic = vi║ deceleration acceleration Ee=me/MiEi section section e.g.: 220 keV electrons cool 400 MeV protons electron temperature kBT 0.1 eV kBT║ 0.1 - 1 meV superposition of a cold momentum transfer by Coulomb collisions intense electron beam cooling force results from energy loss with the same velocity in the co-moving gas of free electrons M. Steck (GSI) CAS 2015, Warsaw Simple Derivation of the Electron Cooling Force electron in reference frame of the beam Analogy: energy loss in matter target (electrons in the shell) faster ion slower ion Rutherford scattering: Energy transfer: Minimum impact parameter: db b from: Energy loss: Coulomb logarithm LC=ln (bmax/bmin) 10 (typical value) M. Steck (GSI) CAS 2015, Warsaw Characteristics of the Electron Cooling Force cooling force F for small relative velocity: vrel -2 for large relative velocity: vrel increases with charge: Q2 2 |F| vrel |F| 1/vrel maximum of cooling force at effective electron temperature M. Steck (GSI) CAS 2015, Warsaw Electron Cooling Time first estimate: (Budker 1967) for large relative velocities cooling time cooling rate (-1): • slow for hot beams -3 • decreases with energy -2 ( is conserved) • linear dependence on electron beam intensity ne and cooler length =Lec/C • favorable for highly charged ions Q2/A • independent of hadron beam intensity for small relative velocities cooling rate is constant and maximum at small relative velocity F vrel = t = prel/F = constant M. Steck (GSI) CAS 2015, Warsaw Models of the Electron Cooling Force • binary collision model description of the cooling process by successive collisions of two particles and integration over all interactions analytic expressions become very involved, various regimes (multitude of Coulomb logarithms) • dielectric model interaction of the ion with a continuous electron plasma (scattering off of plasma waves) fails for small relative velocities and high ion charge • an empiric formula (Parkhomchuk) derived from experiments: M. Steck (GSI) CAS 2015, Warsaw Electron Beam Properties electron beam temperature transverse kBT = kBTcat , with transverse expansion ( Bc/Bgun) 2 longitudinal kBT║ = (kBTcat) /4E0 kBT lower limit : typical values: kBT 0.1 eV (1100 K), kBT║ 0.1 - 1 meV Gun electron beam confined by longitudinal magnetic field (from gun to collector) Collector constant electron beam radius Cooling Section transversely expanded electron beam radial variation of electron energy due to space charge: M. Steck (GSI) CAS 2015, Warsaw Electron Motion in Longitudinal Magnetic Field single particle cyclotron motion cyclotron frequency c = eB/me 1/2 cyclotron radius rc = v/c = (kBTme) /eB electrons follow the magnetic field line adiabatically important consequence: for interaction times long compared to the cyclotron period the ion does not sense the transverse electron temperature magnetized cooling ( Teff T║ T) electron beam space charge: transverse electric field + B-field azimuthal drift electron and ion beam should be well centered Favorable for optimum cooling (small transverse relative velocity): • high parallelism of magnetic field lines B/B0 • large beta function (small divergence) in cooling section M. Steck (GSI) CAS 2015, Warsaw Imperfections and Limiting Effects in Electron Cooling technical issues: physical limitation: Radiative Electron Capture (REC) ripple of accelerating voltage EKIN Continuum magnetic field imperfections M bound states beam misalignment L space charge of electron beam ω and compensation K losses by recombination (REC) loss rate M. Steck (GSI) CAS 2015, Warsaw Examples of Electron Cooling fast transverse cooling at TSR, Heidelberg measured with residual gas ionization beam profile monitor transverse cooling at ESR, Darmstadt cooling of 350 MeV/u Ar18+ ions 0.05 A, 192 keV electron beam profile every 0.1 s. 6 -3 ne = 0.8 ×10 cm cooling of 6.1 MeV/u C6+ ions note! time scale, the cooling time 0.24 A, 3.4 keV electron beam varies strongly with beam parameters n = 1.56 ×107 cm-3 e M. Steck (GSI) CAS 2015, Warsaw Accumulation of Heavy Ions by Electron Cooling standard multiturn injection horizontal vertical fast transverse cooling profile beam size fast accumulation by repeated multiturn injection with electron cooling intensity increase in 5 s by a factor of 10 limitations: space charge tune shift, recombination (REC) M. Steck (GSI) CAS 2015, Warsaw Accumulation of Secondary Particles basic idea: confine stored beam to a fraction experimental verification at ESR of the circumference, inject into gap and apply 54+ cooling to merge the two beam components Xe 154 MeV/u fast increase of intensity (for secondary beams) time fresh injection longit. position injected beam stack stack stack 5x108 4x108 beam current increase 3x108 barrier voltage 2 kV 2x108 1x108 Stacking with Barrier Buckets: Stacked ESR intensity V =120 V, f = 5 MHz, I =0.1 A 0 rf rf e simulation of longitudinal stacking 0 10 20 30 40 50 60 70 80 90 100 with barrier buckets and electron cooling t (s) M. Steck (GSI) CAS 2015, Warsaw Examples of Electron Cooling high energy electron cooling of 8 GeV antiprotons longitudinal cooling with 0.2 A, 4.4 MeV electron beam measured by detection of longitudinal Schottky noise first electron cooling at relativistic energy at Recycler, FNAL resulting in increased luminosity in the Tevatron collider cooling time of some ten minutes has to be compared with the accumulation time of many hours M. Steck (GSI) CAS 2015, Warsaw Electron Cooling Systems High Energy: Low Energy: 35 keV SIS/GSI 4.3 MeV Recycler/FNAL pelletron cooling section 3.4 m long Medium Energy: 300 keV ESR/GSI 20 m long solenoid section M. Steck (GSI) CAS 2015, Warsaw 2. Ionization Cooling energy loss in solid matter proposed for muon cooling acceleration final optimum momentum Large Small emittance emittance Absorber Accelerator not useful for heavy particles Momentum loss is Momentum gain due to strong interaction with matter opposite to motion, is purely longitudinal p, px , p y , E decrease transverse cooling small at absorber in order to minimize multiple scattering large LR, (dE/ds) light absorbers (H2) M. Steck (GSI) CAS 2015, Warsaw Ionization Cooling increased longitudinal cooling by longitudinal-transverse emittance exchange cooling term heating term x x0 + D p/p cooling, if emittance exchange increased longitudinal cooling reduced transverse cooling M. Steck (GSI) CAS 2015, Warsaw Scenarios with Ionization Cooling Muon Collider Neutrino Factory M. Steck (GSI) CAS 2015, Warsaw Scenarios with Ionization Cooling Neutrino Factory (NuMAX) Proton Driver Front End Cool- Accelera on µ Storage Ring n Factory Goal: 1021 m+ & m- per year ing µ+ ν within the accelerator 5 GeV acceptance l t r r . e g e l 0.2–1 1–5 r o r e c ν n − t g n o o i e h µ a r n a t l S GeV GeV c h t a n a a o i l c e n T o h L o r m-Collider Goals: u n u R s C C u 281m C u B s t m l e y S 126 GeV a B p s a u l a c a a C c i c - ~14,000 Higgs/yr C h e Accelerators: n A P I D W Single-Pass Linacs Multi-TeV M Lumi > 1034cm-2s-1 Share same complex Muon Collider Proton Driver Front End Cooling Accelera on Collider Ring µ+ ECoM: Muon Collider r l t Higgs Factory r o r g .
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