Extraction from cyclotrons P. Heikkinen
Classification of extraction schemes Linear accelerators Circular accelerators No extraction problem Constant orbit radius (sychrotrons, betatrons) Increasing orbit radius (cyclotrons, synchrocyclotrons) Pulsed electromagnetic fields (Kickers) Resonant (slow ) extraction r = N/3 Stripping by foil (e.g. H - ) Electromagnetic fields Integer resonance r = N Half integer resonance r = N/ (regenerative extraction) Brute force extraction Precessional extraction
Extraction by acceleration Radial increase of the orbit By acceleration By magnetic pumps dr dn dr dn dr dn accel magn dr dn E E g 1 accel R 1 r
Three ways to get a high extraction rate 1. Build cyclotrons with a large average radius (without increasing the maximum energy). Make the energy gain per turn as high as possible 3. Accelerate the beam into the fringe field, where r drops This also calls for high energy gain, since phase slip in the fringe field must be kept small Item 1. Remember that for the same maximum field and the same energy gain per turn dr 1 accel dn R
Item 3. especially important for high energy cyclotrons r Remember: for an isochronous field k r B 1 db dr Field index And e.g. for a 3-sector magnet r 1 k 0.675F 1 tan... So, e.g. for the PSI 580 MeV cyclotron in the isochronous extraction region 1.6 and at the extraction in the fringe field 1. 1 r Factor of in turn separation r
Resonant extraction Normally the radial gain per turn by acceleration in not enough Magnetic perturbations to enhance the turn separation The integer resonance r =N Brute force Bump in the axial field B r, b N cos N N r close to N The beam is driven off centre, maximum additional radial gain per turn being dr dn (brute force) R bn NB 0
For a typical conventional cyclotron (B 0 =1.7 T) a bump of 0.1 mt introduces a radial gain of about 0. mm!! To get a desired turn separation bigger bumps are needed Brute force This method has been used for example in the AEG compact cyclotron Precessional extraction The beam goes through r =1 resonance with a first order perturbation Beam starts to oscillate around its equilibrium orbit with a frequency r 1 r decreases with radius Two consecutive turns oscillate with a slightly different frequency Phase difference between the turns increases Turn separation increases
Bump with a harmonic coil <B harm >=0 Contribution of harmonic coils in three valleys Precession after r =1 resonance
Equilibrium orbit Stable Unstable Radial phase space without a 1st order perturbation
Radial Phase space with a 1st order perturbation Opening in the stable phase space
Phase and amplitude of the perturbation is important!
Phase and amplitude of the harmonic perturbation important Implication: Centering of the beam is also important!
Note: Mono-energetic beam was started from the equilibrium orbit in this tracking! Single turn extraction: Well centered beam Small RF phase width -> phase slits Nice behavior with a proper 1st harmonic perturbation
Crossing of the r = 1 resonance produces a coherent amplitude x c R b B, neff 1 neff 0 1 d r dn At the resonance crossing point The precession introduces a maximum turn separation dr dn precession sin 1 x c r
Half-integer resonance r = N/ (regenerative extraction) Consider a gradient bump N N N N r r g r B cos, Gradient changes focusing properties Changes radial betatron frequency Vogt-Nilsen: frequency shift r r ~ sin 4 cos ~ cos 0 r r N N B N g R r r N N ~ ~,
sin 4 cos ~ cos 0 r r N N B N g R The frequency shift biggest for N r Expand around N r stop band width ~ 0 NB Rg N N N r r r r
Stop-band r = N/. Inside the stopband, the betatron frequency is imaginary which is responsible for exponential amplitude growth
Particle with a positive rotation around the cyclotron centre the betatron oscillation is described by: x o c 1 cos Re r N 45 o c cos Re ~ 45 e Im ~ r ~ N r, max r e The maximum amplitude increase per turn is dx dn x max R g N x NB 0
1. Inside the stop band the amplitude initially grows or decreases exponentially, according to the starting position, but finally ends up growing. Even if r is slightly different from N/, the resonance locks the phase of the oscillation to a fixed value 3. Particles near the central particle hardly move For medium energy cyclotrons r 1 r / cos dependence A negative gradient bump (the peeler) and a positive gradient bump (the regenerator) about 90 o displaced Regenerative extraction is mainly used in synchrocyclotrons
Comparison between integer and half-integer resonance Flat bump, shape not critical No shift of betatron frequency Energy selective Constant radial gain per turn r =1 r =/ Post-resonance acceleration to r =0.8 Gives additional turn separation through precession Gradient bump, shape critical Shift of betatron frequency towards half-integer value Radius selective Exponential growth of radial gain (asymptotically) Remedy against low energy gain per turn and bad beam quality (synchrocyclotrons)
Resonance extraction at high energies Remember: for an isochronous field r 1/1 and / resonances cannot be used Possibilities: 3/ or 4/ resonances Non-linear resonances The first non-linear resonance, the third order resonance, can also be used For a 3-sector cyclotron the r = 3/3 for slow extraction (such as for synchrotrons)
Radial phase space without a 1st order perturbation
Stability of vertical motion in extraction Especially in precessional extraction where r goes through 1 z varies also greatly Can lead to several resonance crossings Amplitude growth In medium energy cyclotrons r = 1, r = z and z = 0.5 = ½ May be crossed before extraction Must limit the radial amplitude, induced by r = 1, to a few mm The coupling resonance r = z depends strongly on the beam quality In cyclotrons this resonance can be crossed easily In sychrocylotrons with poor beam quality some particles are lost
Characteristics of resonances that can cause growth in vertical amplitude
Extraction elements (Harmonic coils) Electrostatic deflector Electromagnetic channel (Passive) focusing channels Stripper
Electrostatic deflector Negative high voltage Gap: a few mm s
Electromagnetic channel Electrostatic deflector
V-shape entrance for the septum effective thickness 0 mm Distribute heat
L. Calabretta Figure.c: view of the ED, with housing and electrode, placed on the hill. Figure.d: view of the ED, with housing and septum, placed on the hill.
L. Calabretta Figure.1: Cross section of SCENT electrostatic deflector. Figure.b: The area occupied by the ED deflector housing is indicated by blue dashed. The reference extraction trajectory, the inner wall of the cryostat and the first M.C. are shown too.
Electrostatic deflector 0 0 0 0 0 1 1 1 1 1, q E q E q E v E B v E vb q mv E v F mv B v E q F k k k Electrostatic field bends the beam outwards Bending radius increases 0 0 0 q E q mv vb q mv q p B k
45 o x =x+r e.g. 45 degree deflector in a homogenous magnetic field 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 x r r 3.4 0.9 1 1 Cyclotron center
Deflector voltage e.g. 100 MeV proton Extraction radius 1 m Needed deflection after 45 degree 15 mm Deflector gap 5 mm 6 Ek 10010 ev E 3.40.015m 10. MV q e1m 0 m Deflector voltage U Ed 10. MV 0.005m 51kV m
Extracted turn Antiseptum Last turn Septum
Electromagnetic channel
High current in the EMC coil Main coil current + booster current
Minimize B at resonance
Passive focusing channel Vertically focusing Horizontally focusing Iron bars are magnetized by the cyclotron magnetic field
Focusing channel Extracted beam travels in the fast decreasing fringe field Horizontally defocusing More focusing by shaping the field (gradient) by passive channels
Remember to minimize the 1st harmonic perturbation in the acceleration area, especially at the resonance r = 1
C35 Permanent Magnet Doublet W. Kleeven
Stripping extraction The extraction efficiency for deflector + EMC is typically 50 90 %. For high intensities activation, vacuum and melting problems For negative ions (H -, d - ) stripping 1 m carbon foil strips both electrons away Charge state -1 -> +1 Efficiency close to 100 % Short distance in the fringing field Less focusing problems Caution! Electromagnetic stripping at high B and high velocity Electron affinity (binding energy) for H - is 0.75 ev
Accelerator Laboratory, Department of Physics, University of Jyväskylä New 0º dipole Stripping extraction for H H Position of the stripper foil Beam out RF 1 Extractor for positive ions RF
W. Kleeven IBA Cyclone 30 Extraction by stripping All energies go to one crossover point by proper foil azimuthal position Place combination magnet at crossover
Accelerator Laboratory, Department of Physics, University of Jyväskylä Position of stripper Beam exit
Accelerator Laboratory, Department of Physics, University of Jyväskylä Stripper 4 carbon foils (16x mm) thickness 1 and m
W. Kleeven H - Extraction by stripping changes sign Good optics Targets in return yoke shielding
Stripping extraction for heavy ions Typically q =q 1 (1.4 4) Initially moderate charge state Limits the maximum energy Motivation High extraction efficiency Naked ion after stripping (no charge distribution) e.g. 300 AMeV Cyclotron proposal (INFN) Easy If not fully stripped then a distribution» Only one charge state has the right trajectory e.g. Dubna
Radial Tie rods Room for the cryostat H.V. for ED1 L. Calabretta H.V. for ED Radial Tie rods Stripper position system Radial Tie rods Proton beam extraction Carbon beam extraction Radial probe Radial Tie rods
L. Calabretta
L. Calabretta
Dubna: Heavy ions
Self-extracting cyclotron IBA (W. Kleeven) Beam extraction is achieved without the use of an electrostatic deflector A small elliptically shaped pole gap (15 mm at extraction ) is used The beam can be accelerated very close (10 mm) to the radial pole edge This allows to reach the radial limit of horizontal beam stability ( r = 0) before beam deceleration sets in
Self-extraction: Realization Small elliptical hill gap allows for sharp radial gradients magnetic septum groove machined in the pole Pole with goove
IBA 14 MeV SE Cyclotron ma extracted = 80 % =300 mmmrad
Beam Separator
Particles exit incoherently from the magnetic field just by acceleration magnetic field shaping is provided to obtain a coherent beam In one of the four poles a groove is machined This provides a magnetic septum And at the same time an extraction channel Harmonic coils near r = 1 enhance the turnseparation at extraction Similar to the precessional extraction method A high power beam catcher collects lost beam that is not well extracted 75 80 % extraction efficiency (14 MeV p)
Multi-Turn vs Single-Turn Extraction Existing high intensity extraction with ESD PSI injector cyclotron Single turn extraction small RF phase width high current density longitudinal space charge Self-Extraction Cyclotron Multi-turn extraction large RF phase width low current density little space charge effects