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Latest Developments in Parametric-resonance Ionization Cooling

m. Muons, Inc. Latest Developments in Parametric-resonance Ionization Cooling. V.S. Morozov 1,2 , A. Afanasev 2,3 , Y.S. Derbenev 4 , R.P. Johnson 2 1 Old Dominion University 2 Muons, Inc. 3 Hampton University 4 Jefferson Lab. m. Muons, Inc. Outline.

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Latest Developments in Parametric-resonance Ionization Cooling

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  1. m Muons, Inc. Latest Developments in Parametric-resonance Ionization Cooling V.S. Morozov1,2, A. Afanasev2,3, Y.S. Derbenev4, R.P. Johnson2 1 Old Dominion University 2 Muons, Inc. 3 Hampton University 4 Jefferson Lab Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010

  2. m Muons, Inc. Outline • Concept of Parametric-resonance Ionization Cooling (PIC) • PIC linear optics requirements • Epicyclic channel for PIC • Twin-helix channel for PIC • Magnetic optics design • G4beamline simulations • Possible practical implementation • Approach to compensating aberrations Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 2

  3. LEMC Scenario m Muons, Inc. Bogacz Dogbones Scheme R.P. Johnson - Dec. 9, 2008 3 MC Design Workshop JLab

  4. New Fernow-Neuffer plot Goal phase space ν = 0.325 GHz λ = 1.0 – 0.8 m ν = 0.65 GHz λ = 0.5 – 0.3 m 100 % @ z = 0 m Study2a 97 % @ z = 40 m 91 % @ z = 49 m REMEX 89 % @ z = 129 m ν = 1.3 GHz λ = 0.3 m 84 % @ z = 129 m 84 % @ z = 303 m PIC PIC + REMEX = factor of ~100 in luminosity  critical for LEMC feasibility • GH2 pressure = 160 atm • 60 μm Be RF window • E ~ 27 MV/m • Detailed parameter will be given in later slide (slide 15) K. Yonehara 12/02/09 4

  5. Ionization Cooling (IC) Principle Angular divergence cooling m Muons, Inc. • Longitudinal cooling by emittance exchange Incident Muon Beam Dipole Wedge absorber Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 5

  6. Parametric-resonance Ionization Cooling (PIC) Concept Parametric resonance induced in muon cooling channel Muon beam naturally focused with period of free oscillations Wedge-shaped absorber plates combined with energy-restoring RF cavities placed at focal points (assuming aberrations corrected) Ionization cooling maintains constant angular spread Parametric resonance causes strong beam size reduction Emittance exchange at wedge absorbers produces longitudinal cooling Resulting equilibrium transverse emittances are an order of magnitude smaller than in conventional ionization cooling m Muons, Inc. Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 6

  7. PIC Principle m Muons, Inc. • Resonant dynamics: angular spread grows while beam size shrinks • Absorbers keep angular spread finite Optics to restore parallel beam envelope Absorbers Beam envelope without absorbers Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 7

  8. PIC Schematic Equilibrium angular spread and beam size at absorber Equilibrium emittance (a factor of improvement) m Absorber plates Parametric resonance lenses w Muons, Inc. Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 8

  9. m Muons, Inc. PIC Optics Requirements • Horizontal free oscillations’ period  x equal to or low-integer multiple of vertical free oscillations’ period  y • Oscillating dispersion • small at absorbers to minimize energy straggling • non-zero at absorbers for emittance exchange • large between focal points for compensating chromatic and spherical aberrations  • Correlated optics: correlated values of  x,  y and dispersion period  D •  x = ny = mD , e.g.  x = 2y = 4D or  x = 2y = 2D • Fringe-field-free design Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 9

  10. Helical Harmonics Practical fringe-field-free approach Periodic solutions of source-free Maxwell equations in vacuum Harmonic of order n given by Total field m Muons, Inc. Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 10

  11. Epicyclic Channel Superposition of solenoid and two different-period transverse helical fields Problem with dynamic aperture m Muons, Inc. Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 11

  12. Consider two dipole helical harmonics (n = 1) of equal strengths with equal-magnitude and opposite-sign wave numbers k1=-k2 = 2/ Field periodic with  = 2/k, Vertical field only in horizontal plane Twin Helix m Muons, Inc. Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 12

  13. Periodic Orbit and Dispersion m Muons, Inc. • Vertical field only in horizontal plane  Periodic orbit in horizontal plane • Horizontal and vertical motion uncoupled • Region of stable transverse motion in both planes • D=  x= 2y= 4  x= 0.25, y= 0.5 Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 13

  14. Periodic Orbit and Tunes m Muons, Inc. • Two dipole helical harmonics only • Periodic orbit determined by locating fixed point in phase space • Betatron tunes from linear transfer matrix for canonical coordinates • y= 1  resonance  use x= 0.25, y= 0.5 Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 14

  15. Adjusting Correlated Optics m Muons, Inc. • Introduce straight quad to redistribute horizontal and vertical focusing • Down side: cannot satisfy correlated optics conditions for both charges • Iteratively adjust Bd and By/x until correlated optics is reached • No success applying same procedure with double helical quad Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 15

  16. Periodic Orbit m Muons, Inc. Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 16

  17. Dispersion and Chromaticity m Muons, Inc. • Dispersion: • Chromaticity: • Scaling pattern: Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 17

  18. G4BL Simulation m Muons, Inc. Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 18

  19. G4BL Optics Test m Muons, Inc. • No absorber and no RF • 105 100 MeV/c - through 100 periods of “twin helix” with correlated optics • Initially parallel beam uniformly distributed with 10  10 cm square Going In Coming Out Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 19

  20. Final Phase Space m Muons, Inc. Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 20

  21. Possible Practical Implementation m Muons, Inc. Layer of positive-helicity helical conductors with cos azimuthal current dependence Layer of negative-helicity helical conductors Normal quad Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 21

  22. Possible Practical Implementation m Muons, Inc. • Adopt existing technology? Layer of positive-tilted loops with cos z longitudinal current dependence Layer of negatively-tilted loops Normal quad Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 22

  23. Reverse EMittance Exchange Another potential application of twin helix channel Longitudinal emittance after PIC smaller than needed for collider Reverse EMittance EXchange (REMEX) Continue resonant regime Reverse wedge gradient to maximize transverse cooling decrements at the cost of antidamping in longitudinal direction Increase dispersion at absorber plates Maintain reasonable relative momentum spread by bunch stretching in the first stage and by beam acceleration in the second stage Another order of magnitude reduction in transverse emittance m Muons, Inc. Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 23

  24. Aberration Compensation Aberration compensation at beam focal points critical and most challenging for PIC Take full advantage of system’s symmetry to reduce number of aberration compensation conditions Compensation of 2nd-order terms with two sextupole harmonics Compensation of 3rd-order terms with three octupole harmonics Conceptually very similar to problem of aberration compensation at collider interaction point m Muons, Inc. Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 24

  25. 2nd-Order Aberrations 2nd-order aberration compensation conditions  Satisfied automatically for symmetric x2and y2and symmetries of D and ns opposite to symmetry of x Compensation of chromatic tune spread and beam smear at focal points Successfully applied this concept to compensate all 2nd- and 3rd-order aberrations at collider interaction point m Muons, Inc. Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 25

  26. Twin Helix Symmetry m Muons, Inc. Symmetry plane Opposite symmetries y x Dx Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 26

  27. Conclusions and Future Plans Designed twin-helix magnetic structure satisfying PIC requirements Confirmed optics properties with GEANT4-based G4beamline simulations Large dynamic aperture suggested by simulations Suggested straightforward possible practical implementations Possible application for REMEX Conduct simulations including RF and absorber wedges Study aberration compensation following well-defined approach Need to introduce transverse coupling for cooling decrement equalization m Muons, Inc. Beam Physics Symposium, Jefferson Lab, Newport News, VA,August 2, 2010 27

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