Extension of Busch’s theorem to particle beams

Article, Preprint English OPEN
L. Groening ; C. Xiao ; M. Chung (2018)
  • Publisher: American Physical Society
  • Journal: Physical Review Accelerators and Beams (issn: 2469-9888)
  • Related identifiers: doi: 10.1103/PhysRevAccelBeams.21.014201
  • Subject: QC770-798 | Physics - Accelerator Physics | Nuclear and particle physics. Atomic energy. Radioactivity
    • ddc: ddc:530

In 1926, H. Busch formulated a theorem for one single charged particle moving along a region with a longitudinal magnetic field [H. Busch, Berechnung der Bahn von Kathodenstrahlen in axial symmetrischen electromagnetischen Felde, Z. Phys. 81, 974 (1926)ZEPYAA0044-3328]. The theorem relates particle angular momentum to the amount of field lines being enclosed by the particle cyclotron motion. This paper extends the theorem to many particles forming a beam without cylindrical symmetry. A quantity being preserved is derived, which represents the sum of difference of eigenemittances, magnetic flux through the beam area, and beam rms-vorticity multiplied by the magnetic flux. Tracking simulations and analytical calculations using the generalized Courant–Snyder formalism confirm the validity of the extended theorem. The new theorem has been applied for fast modeling of experiments with electron and ion beams on transverse emittance repartitioning conducted at FERMILAB and at GSI. Thus far, developments of beam emittance manipulations with electron or ion beams have been conducted quite decoupled from each other. The extended theorem represents a common node providing a short connection between both.
  • References (20)
    20 references, page 1 of 2

    [1] H. Busch, Berechnung der Bahn von Kathodenstrahlen in axial symmetrischen electromagnetischen Felde, Z. Phys. 81 (5) p. 974, (1926).

    [2] M. Reiser, Theory and Design of Charged Particle Beams, Wiley-VCH, Weinheim, 2008, 2nd ed., Chapter 2.

    [3] S.E. Tsimring, Electron Beams and Microwave Vacuum Electronics, John Wiley & Sons, Inc., Hoboken, 2007, Chapters 1 and 3.

    [4] P.T. Kirstein, G.S. Kino, W.E. Waters, Space Charge Flow, McGraw-Hill Inc., New York, U.S.A., 1967, p. 14.

    [5] A.J. Dragt, General moment invariants for linear Hamiltonian systems, Phys. Rev. A 45, 4 (1992).

    [6] K. Floettmann, Some basic features of the beam emittance, Phys. Rev. ST Accel. Beams 6, 034202 (2013).

    [7] Emittance definitions assume mono-energetic beams and refer to fixed position s0 rather to fixed time t0. The particle angle u′ and its transverse mechanical momentum Pu := mγvu are related through Pu = p · u′, where p is the longitudinal mechanical momentum, which is the same for each particle.

    [8] C. Xiao, L. Groening, O. Kester, H. Leibrock, M. Maier, and C. Mu¨hle, Single-knob beam line for transverse emittance partitioning, Phys. Rev. ST Accel. Beams 16, 044201 (2013).

    [9] R. Brinkmann, Y. Derbenev, K. Flo¨ttman, A low emittance, flat-beam electron source for linear colliders, DESY TESLA-99-09, (1999).

    [10] R. Brinkmann, Y. Derbenev, and K. Flo¨ttmann, A low emittance, flat-beam electron source for linear colliders, Phys. Rev. ST Accel. Beams 4, 053501 (2001).

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