RF particle acceleration

Kyrre N. Sjøbæk*

FYS 4550 / FYS 9550 – Experimental high energy physicsUniversity of Oslo, 26/9/2013

* k.n.sjobak(at)fys.uio.noCERN & University of Oslo

RFstructure

Particles

Microwave

s

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!

F⃗=q ( E⃗+ v⃗× B⃗)

SteeringAcceleration

Typical values in particle accelerators: v = c = 3*108 m/s, q = e = 1.6*10-19 Coulomb E = 100 MV/m (CLIC accelerator structure) => F

E = 1.6*10-11 N

B = 8 Tesla (LHC dipole) => F

B = 3.84*10-10 N

Only E can do work: P = v • F => Use electric field

E

FE

q

B FB

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

E z=A (z)∗cos (ω t+ϕ ( z)+θ0)

Amplitude Oscillation

Phase

To get acceleration: Synchronize particles with field Manipulate A(z) and φ(z)

Injection phase

Important quantities: Cavity voltage

Average gradient

V=∫0

LE z(z (t))dz=

∫0

LA (z)cos (ω z

v+ϕ (z)+θ0)dzz=v∗(t−t0);θ0=ω t 0

Injection time

Eacc=VL

Particle travelingalong 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 pillboxas function of time and position

(fundamental oscillation mode TM010

)

E z=A∗cos (ω t+θ0)

Pillbox cavity – field profile

A(z) = 1 V/m , φ(z) = 0, θ = -60°f = 1 GHz, L = 0.1 m, v = c

V ≈ 0.083 V, Eacc

= 0.83 V/m

Blue line: Ez(z) at given time

Red line: Particle position at given time(optimal injection phase)

Field seen by particle atdifferent injection phases θ

E z(z(t))=A cos(ω zv+θ0)

Pillbox cavity – injection phase

Ideal(max energy gain)

θ0=ω t0

Late

Early

Max energy loss

V=∫0

LE z(z (t))dz

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 insideφ=0, θ=-90°

Lcell

= 0.5 m, f = 600 MHz, v = cV ≈ 0.64 V, E

acc = 0.32 V/m

Blue line: Ez(z) at given time

Red line: Particle position at given time

Linac 1 DTL at CERN

Electric field given as

Phase velocity:

Need to synchronizevelocities: v

ph = v

particle

Inject at correct phase

E z=A (z)cos (ω t−k z)

ω t−k z=0, z=v ph t

→v ph=ωk

= 2π f2π/λ

=λ f

λ = 30 cm

=>

vph =

cE

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:

vph

= c

E and B perp., Ez=0

Smooth wave guide: Wave reflected by side walls

Vph

> c

Can have Ez

Periodically loaded wave guide: Wave reflected by side walls and

loading Design for wanted

k and frequency => vph

Can have Ez

Animations by Erk Jensen

Field in free space

+=

Field in sm

ooth 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

SLA

C S

LC structure,

2.856 GH

zCLIC damped structure,

11.9942 GHz

Periodically loaded waveguide

Structure:CLIC_G

middle cell, repeated 6

times

f = 11.9942 GHzd = 8.3037 mm

Ψ = 120°

v = vph

= c

Dashed lines: disc loads(“Irises”)

Wake fields:Beam-field interaction

Acceleration => energy transferfrom field → particle

Field amplitude decreased

Particle “leaving behind” electromagnetic wake field,

Interferes destructivelywith 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 deviceswith limited lifetime

Pulsed devices

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

RFR= pqB

= γmcqB

P∝ E4

m4R2

τrevolution=h τRF⇒ f RF=h f revolution 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 particlesgo faster

(2)High energy particles larger bending radius=> Travel longer

V=∫0

LE z(z (t))dz=V 0 cos(Δθ)

Δθ = 0

LateEarly

V0

LHC: 1011 protons/bunch

Stabilizing mechanism:Low energy => more acceleration; high energy => less acceleration

Lowenergies

Highenergies

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 tostay inside their bucket

?? QUESTIONS ??

V=∫0

LE z(z (t))dz=∫0

LA (z)cos (ω z

v+ϕ (z)+θ0)dz

Backup

More RF accelerator types:Widerøe linac

Apply alternating field to array of electrodes

Electric field between electrodesaccelerates particles

Synchronicity:

Large losses due to RF radiation

Used for low-velocity structures

L=v∗t=v 12

τ= v2f

Wake fields Two types:

Longitudinal:Accelerates / decelerates beam

Transverse:Kicks beam sideways

Structures havemultiple 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

Lon

gitu

din

al

Tra

nsverse

Wake fields (long+trans)

Damping wave guides (extended)