1. Cyclotrons Mike Seidel Paul Scherrer Institut
CERN accelerator school – introductory course
Prague, Czech Republic, Sep 12, 2014
Mike Seidel
Paul Scherrer Institut

2. Cyclotrons - Outline the classical cyclotron
history of the cyclotron, basic concepts and scalings, classification of cyclotron-like accelerators
separated sector cyclotrons
focusing in Thomas-cyclotrons, spiral angle, classical extraction: pattern/stepwidth, transv./long. space charge
cyclotron subsystems
extraction schemes, RF resonators, magnets, vacuum issues, instrumentation
applications and examples of existing cyclotrons
TRIUMF, RIKEN SRC, PSI Ring, PSI medical cyclotron
discussion
Classification of circular accelerators
Pro’s and Con’s of cyclotrons for different applications
in this presentation I will give an overview on physics and technology of cyclotrons
the first half of this presentation will focus on theoretical aspects; first the basic concepts of cyclotrons will be introduced together with a short description of the historical developments; and then beam dynamics aspects like how a clean extraction can be realized; space charge effects; ion induced desorption; numerical modelling
the second half is dedicated to more practical aspects as cyclotron subsystems, examples of realized machines; finally a brief summary on Pro’s and Con’s of cyclotrons
Let me say that the theme is rather broad, and I had to pick out topics which I think are relevant for high intensity operation. Of course this presentation cannot really be comprehensive, and naturally I am biased a bit by the PSI machine which produces a MW proton beam.

3. The Classical Cyclotron
powerful concept:
simplicity, compactness
continuous injection/extraction
multiple usage of accelerating voltage
two capacitive electrodes „Dees“, two gaps per turn
internal ion source
homogenous B field
constant revolution time
(for low energy, 𝛾~1)
first cyclotron:
1931, Berkeley
1kV gap-voltage
80kV Protons
E.Lawrence & S.Livingston,
27inch Zyklotron
John Lawrence (center), 1940’ies
first medical applications: treating patients with neutrons generated in the 60inch cyclotron
Here is a reminder about the classical cyclotron concept. This concept already has features that make the cyclotron suited for high power operation. The continuous operation, meaning non-cycling is very important. Also the resonant acceleration feature is a key, meaning that the voltages that must be handled are comparable low.
As you probably know, difficulties arise in theis concept due to the insufficient vertical focusing.

4. cyclotron frequency and K value
cyclotron frequency (homogeneous) B-field:
cyclotron K-value:
→ K is the kinetic energy reach for protons from bending strength in non-relativistic approximation:
→ K can be used to rescale the energy reach of protons to other charge-to-mass ratios:
→ K in [MeV] is often used for naming cyclotrons
examples: K-130 cyclotron / Jyväskylä
cyclone C230 / IBA

5. classical cyclotron - isochronicity and scalings
continuous acceleration  revolution time must stay constant, though Ek, R vary
magnetic rigidity:
radius increment per turn decreases with increasing energy
→ extraction becomes more and more difficult at higher energies
orbit radius from isochronicity:
deduced scaling of B:
thus, to keep the isochronous condition, B must be raised in proportion to (R); this contradicts the focusing requirements (discussed later)
this slide contains some fundamental relations which we need later for some derivations…

6. field index
the field index describes the (normalized) radial slope of the bending field:
from isochronous condition:
B; R

7. equation of motion in a classical cyclotron
centrifugal force mv2/r
Lorentz force qvB
focusing: consider small deviations x from beam orbit R (r = R+x):

8. betatron tunes in cyclotrons
thus in radial plane:
note: simple case for k = 0: r = 1
(one circular orbit oscillates w.r.t the other)
using Maxwell to relate Bz and BR:
k<0 to obtain vertical focus.
in vertical plane:
thus: in classical cyclotron k < 0 required;
however this violates isochronous condition k = 2-1 > 0

9. classification of cyclotron like accelerators
classical cyclotron
[B() = const]
complexity
Thomas cyclotron
[Azimuthally Varying Field,
isochronous, one pol]
AVF concept – harmonic pole shaping,
electron model, Richardson et al (1950),
courtesy of Lawrence Berkeley National Laboratory
separated sector cyclotr.
[isochronous, separated magnets, resonators]
synchro-cyclotron
[varying RF frequency]
Fixed Focus Alternating Gradient Accelerator FFAG
[varying RF, strong focusing]
high intensity
high energy
compact machine

10. next: sector cyclotrons
AVF vs. separated sector cyclotron
focusing in sector cyclotrons
extraction: pattern/stepwidth
transv./long. space charge

11. focusing in sector cyclotrons
hill / valley variation of magnetic field (Thomas focusing) makes it possible to design cyclotrons for higher energies
Flutter factor:
with flutter and additional spiral angle
of bending field:
[illustration of focusing at edges]

12. Azimuthally Varying Field vs. Separated Sector Cyclotrons
PSI Ring cyclotron
PSI/Varian comet: 250MeV sc. medical cyclotron
AVF = single pole with shaping
often spiral poles used
internal source possible
D-type RF electrodes, rel. low energy gain
compact, cost effective
depicted Varian cyclotron: 80% extraction efficiency; not suited for high power
modular layout, larger cyclotrons possible, sector magnets, box resonators, stronger focusing, injection/extraction in straight sections
external injection required, i.e. pre-accelerator
box-resonators (high voltage gain)
high extraction efficiency possible:
e.g. PSI: 99.98% = (1 - 2·10-4)

13. derivation of turn separation in a cyclotron
starting point: bending strength for p
compute total log.differential
use field index k = R/BdB/dR
radius change per turn
[Ut = energy gain per turn]
isochronicity not conserved (last turns)
the radial orbit increment per turn is an extremely important quantity for cyclotrons with electrostatic extraction elements, which is the classical extraction method.
to derive the scaling of this stepwidth we start with the bending strength; the three variable B,R and energy are related by this equation
an additional relation is given by the isochonicity condition, and this allows us to eliminate the dependence on the slope of the B-field
isochronicity conserved (general scaling)

14. turn separation - discussion
for clean extraction a large stepwidth (turn separation) is of utmost importance; in the PSI Ring most efforts were directed towards maximizing the turn separation
desirable:
limited energy (< 1GeV)
large radius Rextr
high energy gain Ut
general scaling at extraction:
scaling during acceleration:
illustration:
stepwidth vs. radius in cyclotrons of different sizes; 100MeV inj  800MeV extr
here I want to summarize the important result and show a numerical example, to give you a feeling on what can be achieved in practice
the turn separation of an isochronous cyclotron at extraction can be written in this way: proportional to the extraction radius, the energy gain per turn and inversely proportional to gamma^third power for large gamma…
for low energies it can be approximated in this way, and since beta is propto R we see that during the acceleration process the turn separation becomes smaller like 1/R
here are numerical examples for cyclotrons accelerating from 100 to 800 MeV, with different field strength, that is different sizes. typical stepwidth´s are of the order of 5mm; we see that the stepwidth decreases roughly like 1/R through acceleration, however the final spewidth at extraction increases linearly with the size of the cyclotron; thus one should not try to accelerate very high intensity beams with a very compact cyclotron

15. extraction with off-center orbits
betatron oscillations around the “closed orbit” can be used to increase the radial stepwidth by a factor 3 !
without orbit oscillations: stepwidth from Ek-gain (PSI: 6mm)
with orbit oscillations: extraction gap; up to 3 x stepwidth possible for r=1.5 (phase advance)
beam to extract
particle density
it is possible to increase the turn separation in a cyclotron by injecting the beam off-center to induce a radial orbit oscillation around the closed orbit
on the upper plot you see an idealized beampattern without such oscillations, whereas on the lower plot such oscillations are considered; below you see the rotating phase space vector of the orbit center; the horizontal tune corresponds to the number of rotations per turn; the steep decrease of the tune at the outer edge is essential [explain the three turns; third last would be closer to last if 0.5 and not 0.75]
with a radial tune of 1.5 an increase of the stepwidth by a factor 3 can be achieved; this is gain is equivalent to a three times larger cyclotron
--- this plot shows how we decrease the horizontal tune at the extraction energy in the PSI Ring cyclotron
radial tune vs. energy (PSI Ring)
typically r ≈  during acceleration; but decrease in outer fringe field r
phase vector of orbit oscillations (r,r’)

16. extraction profile measured at PSI Ring Cyclotron
turn numbers
red: tracking simulation [OPAL]
black: measurement
dynamic range:
factor in particle density
this is a measurement of the beam density at extraction on a logarithmic scale; the black line; the red line is a simulation using the OPAL tracking program; the beam centroid positions are indicated as well; you see that we achieve a suppression of the particle density at the location of the septum by 3 orders of magnitude
position of extraction septum
d=50µm
[Y.Bi et al]

17. longitudinal space charge
sector model (W.Joho, 1981):
 accumulated energy spread transforms into transverse tails
consider rotating uniform sectors of charge (overlapping turns)
test particle “sees” only fraction of sector due to shielding of vacuum chamber with gap height 2w 2w F
two factors are proportional to the number of turns:
the charge density in the sector
the time span the force acts
derivation see: High Intensity Aspects of Cyclotrons, ECPM-2012, PSI
in addition:
3) the inverse of turn separation at extraction:
next I want to discuss space charge effects, the longitudinal space charge first
we go through a rather simplified analytical calculation; of course numerical methods are more precise, however the underlying principles and scalings cannot be demonstrated with computer models
I repeat here the sector model, which was introduced by werner joho back in 1981; the goal of the calculation is to estimate the energy change that heading and trailing particles receive from the repelling space charge forces of the bunch center
we assume overlapping turns and constant charge density in the resulting rotating sectors of charge; a test particle at the head of the bunch will not see the whole sector due to shielding effects of the vacuum chamber; we assume the charge within a radius w will contribute and this radius stays constant throughout the acceleration process; on the other hand the charge density varies
[explain derivation]
► thus the attainable current at constant losses scales as nmax-3

18. longitudinal space charge; evidence for third power law
at PSI the maximum attainable current indeed scales with the third power of the turn number
maximum energy gain per turn is of utmost importance in this type of high intensity cyclotron
 with constant losses at the extraction electrode the maximum attainable current indeed scales as: 𝑰 𝐦𝐚𝐱 ∝𝒏 𝒕 −𝟑
indeed we observed this scaling at PSI; we achieved the major intensity increase within a fixed geometry but a steady increase of the circumference voltage, that is better RF amplifiers and resonators
historical development of current and turn numbers in PSI Ring Cyclotron

19. transverse space charge
with overlapping turns use current sheet model!
vertical force from space charge:
[constant charge density, Df = Iavg/Ipeak]
focusing force:
thus, eqn. of motion:
 equating space charge and focusing force delivers an intensity limit for loss of focusing!
transverse concerns the radial and vertical coordinates; significant is the change in the focusing frequency of the particles and thus we consider here the vertical force, since the vertical focusing is most critical in a cyclotron
for the calculation we use again the sector model with the simplified assumption of constant charge density with the rotating sector of beam particles; in this case the vertical force is a linear function of y; again the particle density contains the stepwidth DR; on the other hand the focusing force from the magnet lattice is given by this expression
the following equation of motion results; we see the repelling space charge force weakens the magnet focusing; in the extreme case the term in brackets vanishes; in practice problems occur earlier for significant tune shifts, lets say of 0.4
tune shift from forces:

20. next: cyclotron subsystems
extraction schemes
RF systems/power efficiency
cyclotron magnets
comments on vacuum
specific instrumentation
in the next section I will give a brief overview on cyclotron subsystems which are of relevance for high intensity operation

21. injection/extraction schemes
deflecting element should affect just one turn, not neighboured turn  critical, cause of losses
often used: electrostatic deflectors with thin electrodes
alternative: charge exchange, stripping foil; accelerate H- or H2+ to extract protons (problem: significant probability for unwanted loss of electron; Lorentz dissociation: B-field low, scattering: vacuum 10-8mbar)
binding
energies H-
H2+
0.75eV
15eV
two major schemes exist to realize the extraction of high intensity beams from cyclotrons; I mentioned many times the scheme that utilizes an electrostatic deflector
an alternative is to accelerate ions that carry electrons and strip these electrons using an extraction foil; with H- the charge can be changed to H+ which reverses the deflection angle in a magnetic field; H2+ has the advantage of a higher binding energy of the electron and thus lower random losses; however the charge to mass ratio is ½ requiring stronger magnets and the extraction scheme is more difficult since the bending radius changes by two but dos not change polarity when this electron is stripped -
foil HV
extraction by charge exchange in foil
eg.: H-  H+
H2+  2H+
extraction electrode
placed between turns

22. injection/extraction with electrostatic elements
parameters extraction chan.:
Ek= 590MeV
E = 8.8 MV/m
= 8.2 mrad
= 115 m
U = 144 kV
principle of extraction channel
major loss mechanism is scattering in 50m electrode!
injection element in Ring
Tungsten stripes
electrostatic rigidity:
the conceptional drawing shows the electrostatic extraction channel in the PSI Ring cyclotron; we have a cathode which is negatively charged against ground; the anode is made from thin tungsten stripes, 50um; tungsten can withstand high temperatures, that is when the electrode is accidentally hit by the beam; the gap is 16mm, the voltage 140kV and the deflection angle 8mrad; in addition the element has s mall collimator and several stripes for diagnostic purposes
the foto shows the injection element that exhibits a similar layout

23. extraction foil
thin foil, for example carbon, removes the electron(s) with high probability
new charge state of ion brings it on a new trajectory → separation from circulating beam
lifetime of foil is critical due to heating, rad.damage; conversion efficiencies, e.g. generation of neutrals, must be considered carefully
How much power is carried by the electrons?
stripped electrons deposit energy in the foil B H- H+ e
foil
 1/2000 of beam power
for the stripping scheme one needs an extraction foil and here I give a few comments on that
of course also the extraction foil undergoes a high thermal stress; fatigue effects, sublimation and radiation damage are issues
also the conversion efficiency is not perfect; the small probabilities for the generation of unwanted charge states must be considered
Bending radius of electrons?
 typically mm

24. example: multiple H- stripping extraction at TRIUMF
[R.Baartman]
here you see a sketch of the multiple extraction paths in the TRIUMF cyclotron; this machine accelerates H- ions which can be extracted at different radii, that means energies, and locations; you see how the bending radius changes polarity

25. example: H2+ stripping extraction in planned Daedalus cyclotron [neutrino source]
purpose: pulsed high power beam for neutrino production
800MeV
5MW
the DAEDALUS cyclotron is presently planned to drive neutrino production targets; H2+ is chosen due to advantages in space charge effects, and the possibility of stripping extraction
here is an example for H2+ stripping extraction; by stripping the sign of the charge does not change, however the bending radius is halved at the foil
[L.Calabretta, A.Calanna et al]

26. components: cyclotron resonators
cyclotron resonators are basically box resonators
resonant frequency:
beam passes in center plane;
accelerating voltage varies as sin(r)
now I switch from the extraction problem to the problem of acceleration; in separated sector cyclotrons we use closed box resonators that are installed inbetween the magnets
the concept is shown here; frequency depends not on the width of the resonator; note the sine like voltage dependence

27. cross sections of PSI resonators
hydraulic tuning
new
old 4m 2m 0m
loop 50MHz
beam(s)
here you see cross sections of the original aluminum resonators of the psi ring from the 70’s and the newer Cu resonators right; we save power and achieve higher gap voltages; loop coupler are robust and allow high power transfer; tuning against outer air pressure changes is necessary; hydraulic devises achieve a 20um resolution
original Al-Resonator
Oper. freq. = 51 MHz
Max. gap voltage = 760 kV
Power dissipation = 320 kW
Q0 = 32'000 (meas. value)
new Cu-Resonator
Oper. freq. = 51 MHz
Max. gap voltage > 1MV
Power dissipation = 500 kW
Q0  48'000

28. copper resonator in operation at PSI’s Ring cyclotron
f = 50.6MHz; Q0 = 4,8104; Umax=1.2MV (presently 0.85MV)
transfer of up to 400kW power to the beam per cavity
Wall Plug to Beam Efficiency (RF Systems): 32%
resonator inside
hydraulic tuning devices (5x)
pictures of the resonators during production and in finalized condition

29. components: sector magnets
cyclotron magnets typically cover a wide radial range  magnets are heavy and bulky, thus costly
PSI sector magnet
iron weight: 250 tons
coil weight: 28 tons
orbit radius: 2.1…4.5 m
spiral angle: 35 deg

30. components: sector magnets
focusing and isochronicity need to be precisely controlled  sophisticated pole shaping including spiral bounds, many trim coil circuits
modern cyclotrons use superconducting magnets; but for high intensity compactness is generally disadvantageous
field map of PSI Ring
magnet weight vs. energy reach for different cyclotrons
Joho, CAS Aarhus, 1986
superconducting

31. cyclotron vacuum system
vacuum chamber with large radial width  difficult to achieve precisely matching sealing surfaces noticeable leak rates must be accepted
use cryo pumps with high pumping speed and capacity
≈10-6mbar for p, ≈10-8mbar for ions (instability! e.g. AGOR at KVI)
design criterion is easy access and fast mountability (activation)
example: inflatable seals installed between resonators; length: 3.5m
O-ring grooves
evacuated intermittent volume
length: 3.5m
few comments on vacuum
one difficulty for cyclotrons is large radial width of the vacuum chamber, for example in comparison to synchrotrons or FFAG’s; I explained to you that on the other hand the continuous acceleration feature is essential for high power operation
the wide and complicated chamber with tight space requirements and in addition activation makes the design of the vacuum system rather special and difficult….
example inflating seals; small space; simply and quickly removable; activation!

32. cyclotron instrumentation example: PSI 72MeV injector cyclotron
phase probes
«RF pickups»
injection channel
transverse probes
«wire scanners»
extraction channel

33. instrumentation: radial probe for turn counting / orbit analysis
wire scanner with three tilted wires delivers radial beam profile and some vertical information
radial: positions of individual turns
vertical/radial orbit positions and stored reference orbit (crosses)
«pseudo tomography» with tilted wires

34. next: cyclotron examples
TRIUMF, RIKEN SRC, PSI-HIPA, PSI-Comet
next I show you a few pictures and really basic information from selected existing cyclotrons

35. comparison of cyclotrons
TRIUMF
RIKEN SRC (supercond.)
PSI Ring
PSI medical (supercond.)
particles
H-  p
ions p
K [MeV]
520
2600
592
250
magnets (poles)
(6) 6 8
(4)
peak field strength [T]
0.6
3.8
2.1
Rinj/Rextr [m]
0.25/3.8…7.9
3.6/5.4
2.4/4.5
-/0.8
Pmax [kW]
110
1 (86Kr)
1300
0.25
extraction efficiency
(tot. transmission)
0.9995
(0.70)
(0.63)
0.9998
0.80
extraction method
stripping foil
electrostatic deflector
comment
variable energy
ions, flexible
high intensity
compact

36. cyclotron examples: TRIUMF / Vancouver
photo: iron poles with spiral shape
(max=70deg)
p, 520MeV, up to 110kW beam power
diameter: 18m (largest n.c. cyclotron worldwide)
extraction by stripping H-  variable energy; multiple extraction points possible
the figure shows the TRIUMF cyclotron in the construction phase; the spiral shape of the iron is nicely visible

37. RIKEN SRC in the vault

38. examples: PSI High Intensity Proton Accelerator
Ring Cyclotron 590 MeV
2.2mA / 1.3MW
diameter: 15m
SINQ
spallation source
meson production targets
the psi cyclotron complex has a long history; a chain of two cyclotrons generates a 1.3MW proton beam; in the last year we even obtained 1.4MW in several test shifts
the beam generates muons an neutrons for solid state physics and particle physics experiments
dimensions:
120 x 220m2
proton therapie center [250MeV sc. cyclotron]

39. superconducting coils
250 MeV proton cyclotron (ACCEL/Varian)
ACCEL
Closed He system
4 x 1.5
300 kW
90 tons
Proton source
superconducting coils
=> T
1.4 m
4 RF-cavities
≈100 kV on 4 Dees
3.4 m

40. compact cyclotrons for Isotope production
vertical setup (!)

41. finally: discussion comparison of circular accelerators
suitability of cyclotrons
some literature

42. classification of circular accelerators
bending radius
bending field vs. time
bending field vs. radius
RF frequency vs. time
operation mode (pulsed/CW)
betatron
induction
microtron
varying h
classical cyclotron
simple, but limited Ek
isochronous cyclotron
suited for high power!
synchro- cyclotron
higher Ek, but low P
FFAG
strong focusing!
a.g. synchrotron
high Ek, strong focus
this table shows a classification of circular accelerator with respect to several features of the bending field and the temporal behaviour
for example the betatron in the first line is an induction accelerator, which means the acc voltage is generated by the time variation of the bending field; the radius stays constant; the radial slope of the bending field provides stability; however the field must be cycled which strongly limits the attainable average beam current
I cannot go through all concepts, but what you can keep from this slide is that the isochronous cyclotron is best suited, since it allows CW operation, has sufficient focusing to reach reasonably high energies, and can achieve low losses in the 10e-4 region

43. pro and contra cyclotron
limitations of cyclotrons
typical utilization of cyclotrons
energy limitation ≈1GeV due to relativistic effects
relatively weak focusing is critical for space charge effects (10mA ?)
tuning is difficult; field shape; many turns; limited diagnostics
wide vacuum vessel (radius variation)
medical applications 250MeV; intensity range well covered
isotope production  several 10MeV
acceleration of heavy ions (e.g. RIKEN)
very high intensity proton beams (PSI:1.4MW, TRIUMF: 100kW, ADS Concepts )
one slide with some selected arguments pro and contra cyclotrons…
injection and extraction are critical since typically one has to place material close to the beam, which causes losses by scattering; in a sc linac in comparison the aperture is large and you have no extraction issues

44. cyclotron conferences – a valuable source of knowledge
cyclotron conferences every three years
first 1959
old cyclotron conferences are digitized for JACOW (effort of M.Craddock!)
cyclotrons 2016: organized by PSI in Zürich

45. some literature w.r.t. cyclotrons
comprehensive overview on cyclotrons
L.M.Onishchenko, Cyclotrons: A Survey, Physics of Particles and Nuclei 39, 950 (2008)
scaling of PSI concept to 10MW
Th.Stammbach et al, The feasibility of high power cyclotrons, Nuclear Instruments and Methods in Physics Research B 113 (1996) 1-7
space charge effects and scalings
W.Joho, High Intensity Problems in Cyclotrons, Proc. 5th intl.
Conf. on Cyclotrons and their Applications, Caen, (1981)
long. space charge; comparison to analytical result
E.Pozdeyev, A fast code for simulation of the longitudinal space charge effect in isochronous cyclotrons, cyclotrons (2001)
H2+ concept for high power
L.Calabretta et al, A multi megawatt cyclotron complex to search for cp violation in the neutrino sector, cyclotrons (2010);
upcoming NIM paper!
OPAL simulations; documentation
J.Yang, A. Adelmann, et al. Phys. Rev. STAB Vol. 13 Issue 6 (2010)
cyclotrons 2013 conference Vancouver
conference summary:

46. thank your for your attention !