RF particle acceleration Kyrre N. Sjøbæk * FYS 4550 / FYS 9550 – Experimental high energy physics University of Oslo, 26/9/2013 *k.n.sjobak(at)fys.uio.no CERN & University of Oslo RF structure Particles Microwaves

Outline Accelerating a charged particle beam  DC/RF RF acceleration details Types of RF accelerating structures  Alvarez Drift Tube Linac (DTL)  Traveling wave Wakefields Microwave power production Longitudinal dynamics in circular accelerators

Accelerating charged particles Forces of nature:  Gravity – TO WEAK  Strong & weak nuclear force – SHORT RANGE  Electromagnetic – OK! SteeringAcceleration Typical values in particle accelerators:  v = c = 3*10 8 m/s, q = e = 1.6* Coulomb  E = 100 MV/m (CLIC accelerator structure) => F E = 1.6* N  B = 8 Tesla (LHC dipole) => F B = 3.84* N Only E can do work: P = v F => Use electric field E FEFE q B FBFB

Applying the electric field Constant voltage (DC)  Used in Van de Graaff generators, electron tubes, and first stages of accelerators  Energy = q*V  Can't go to very high energies High voltages creates sparks =>Maximum some MegaVolts Circular accelerators not possible DC RF

Applying the electric field – RF Time-varying field (RF)  Less chance of sparks  Can go to high energies AmplitudeOscillation Phase To get acceleration: Synchronize particles with field Manipulate A(z) and φ(z) Injection phase Important quantities:  Cavity voltage  Average gradient Injection time Particle traveling along the z axis

Pillbox cavity Circular cavity with constant radius A(z), φ(z) constant Theoretical cavity: No openings for power or beam Similar to many standing-wave cavities Electric field in pillbox as function of time and position (fundamental oscillation mode TM 010 )

Pillbox cavity – field profile A(z) = 1 V/m, φ(z) = 0, θ = -60° f = 1 GHz, L = 0.1 m, v = c V ≈ V, E acc = 0.83 V/m Blue line: E z (z) at given time Red line: Particle position at given time (optimal injection phase) Field seen by particle at different injection phases θ

Pillbox cavity – injection phase Ideal (max energy gain) Late Early Max energy loss

Alvarez Drift Tube Linac (DTL) Long “pillbox” resonator Hollow cylinders where the particles “hides” while field reverses Often used in for low energies E = 0 inside drift tubes E α sin(ωt) in gaps CERN Linac 4 DTL prototype Increasing period as particle accelerates

Alvarez Drift Tube Linac (DTL) A=1 V/m (outside drift tubes), 0 V/m inside φ=0, θ=-90° L cell = 0.5 m, f = 600 MHz, v = c V ≈ 0.64 V, E acc = 0.32 V/m Blue line: E z (z) at given time Red line: Particle position at given time Linac 1 DTL at CERN

Electric field given as Phase velocity: Need to synchronize velocities: v ph = v particle Inject at correct phase λ = 30 cm => v ph = c E acc = A(z) λ = 60 cm => v ph = 3*c Remember: k = 2π/λ (wavenumber / spatial angular frequency) ω = 2πf (angular time frequency) f = 1 GHz, A = 1 V/m, v particle = c Traveling wave acceleration

Synchronized traveling waves EM waves in free space:  v ph = c  E and B perp., E z =0 Smooth wave guide:  Wave reflected by side walls  V ph > c  Can have E z Periodically loaded wave guide:  Wave reflected by side walls and loading  Design for wanted k and frequency => v ph  Can have E z Animations by Erk Jensen Field in free space + = Field in smooth waveguide

Periodically loaded waveguide Disc loaded waveguide Traveling wave reflected by disks Used at high-energy linear accelerators RF in Beam in Accelerating structure Period d Main parameters: Frequency Period d Beam in RF in RF out Phase advance/period Number of periods RF out Beam out

Periodically loaded waveguide SLAC SLC structure, GHz CLIC damped structure, GHz

Periodically loaded waveguide Structure: CLIC_G middle cell, repeated 6 times f = GHz d = mm Ψ = 120° v = v ph = c Dashed lines: disc loads (“Irises”)

Wake fields: Beam-field interaction Acceleration => energy transfer from field → particle Field amplitude decreased Particle “leaving behind” electromagnetic wake field, Interferes destructively with accelerating field Beam loading

Powering accelerator structures: Klystrons (the conventional way) Klystron tube: narrowband microwave amplifier  Amplification: ~100 W -> 10 MW  Input voltage: ~100 kV Most efficient at long pulses, ~1 GHz frequencies Complex devices with limited lifetime P u ls e d d e vi c e s From radartutorial.eu

Powering accelerator structures: Drive beam (the CLIC way) Decelerate “drive beam”, extract energy from beam to microwaves  Drive beam: 12 GHz high current / low energy beam Deceleration by wakefield in “PETS” structures Works efficiently at high power, high frequency, short pulses “Beam transformer”

Circular accelerators: (synchrotrons) Sends beam on a repeating orbit Re-using RF cavities Energy limited by  Bending magnet strength  Synchrotron radiation Beam must be synchronous with RF RF h = harmonic number (integer)

Synchrotron longitudinal dynamics Accelerate bunches of particles  Spread in energy  Spread in position z => Arrival at different times to RF cavities Two competing processes (1)High energy particles go faster (2)High energy particles larger bending radius => Travel longer Δθ = 0 Late Early V0V0 LHC: protons/bunch Stabilizing mechanism: Low energy => more acceleration; high energy => less acceleration Low energies High energies

Summary Particle acceleration using electric field Create & store field in RF resonators Need to synchronize particle “bunches” with RF phase Cavity voltage: RF longitudinal stability forces the particles to stay inside their bucket ?? QUESTIONS ??

Backup

More RF accelerator types: Widerøe linac Apply alternating field to array of electrodes Electric field between electrodes accelerates particles Synchronicity: Large losses due to RF radiation Used for low-velocity structures

Wake fields Two types:  Longitudinal: Accelerates / decelerates beam  Transverse: Kicks beam sideways Structures have multiple modes of oscillation  Different modes have different frequencies  Can be exited by frequency content of beam (shorter bunches => higher frequencies) Energy in wake field can heat up equipment inside vacuum chamber  Wakes produced wherever the vacuum chamber is changing cross-section Longitudinal Transverse

Wake fields (long+trans)

Damping wave guides (extended)