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## Emittance in addition to Emittance Measurements S. Bernal

Haynes, William, Finance Reporter has reference to this Academic Journal, PHwiki organized this Journal Emittance in addition to Emittance Measurements S. Bernal USPAS 08 U. of Maryl in addition to , College Park Introduction: Phase in addition to Trace Spaces, Liouvilles theorem, etc. Liouvilles Theorem: area conserved in either G or m spaces as long as Hamiltonian systems Units of area in Phase Space (m-space) are those of Angular Momentum. Units of area in Trace Space are those of length: metre (angle measure is dimensionless). Review of Courant-Snyder Theory b(s) is a lattice function that depends on k0 (s), but A in addition to are different as long as different particles. The ellipse equation defines self-similar ellipses of area pAX2 at a given plane s. The largest ellipse defines the beam emittance through

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Space charge in addition to emittance (M. Reiser, Chap. 5) If linear space charge is included, then k0(s)k(s) in addition to the b function is no longer just a lattice function because it now depends on current also. b becomes a lattice+beam function. The emittance above is the effective or 4rms emittance (also called edge emittance) which is equal to the total (100%) emittance as long as a K-V distribution. Further, adding space charge does not require changing the emittance definition Emittance in addition to current are independent parameters in the envelope equation: For a Gaussian distribution, the total in addition to RMS emittances are equal when the Gaussian is truncated at 1-s. RMS Emittance in addition to Envelope Equation (Pat G. OShea) Emittance Growth (M. Reiser, Chap. 6) The normalized emittance is an invariant: If initial transverse beam distribution is not uni as long as m, rms emittance grows in a length of the order of lp/4. If initial beam envelope is not rms-matched, rms emittance grows in a length of the order of lb.

Laminar in addition to Turbulent Flows Transverse Emittance Measurement Techniques Basic Optics I

Basic Optics II Pepper-Pot Technique 10keV, 100 mA, 700 experiment X = 67 m, Y = 55 m Pepper-Pot Technique

Calculating emittance in addition to plotting phase space: Pepper-Pot Technique Beam (s) in addition to Transfer (R) Matrices Define the beam matrix as long as , say, x-plane: Consider 2 planes z0 in addition to z1, z1>z0. Particle coordinates trans as long as m as: R is the Transfer matrix. Then, the beam matrix is trans as long as med according to: Quadrupole Scan

Quadrupole Scan: results as long as 6 mA beam References Martin Reiser, Theory in addition to Design of Charged-Particle Beams, 2nd Ed, Secs. 3.8.2, 5.3.4 (see Table 5.1) in addition to Chapter 6. 2 D. A. Edwards in addition to M. J. Syphers, An Introduction to the Physics of High Energy Accelerators, Sec. 3.2.4 (see Table 3.1). Claude Lejeune in addition to Jean Aubert, Emittance in addition to Brightness: Definitions in addition to Measurements, Advances in Electronics in addition to Electron Physics, Supplement 13A, Academic Press (1980). Andrew M. Sessler, Am. J. Phys. 60 (8), 760 (1992); J. D. Lawson, The Emittance Concept, in High Brightness Beams as long as Accelerator Applications, AIP Conf. Proc. No. 253; M.J. Rhee, Phys. Fluids 29 (1986). Michiko G. Minty in addition to Frank Zimmermann, Beam Techniques, Beam Control in addition to Manipulation, USPAS, 1999. 6. S. G. Anderson, J. B. Rosenzweig, G. P. LeSage, in addition to J. K. Crane, Space-charge effects in high brightness electron beam emittance measurements, PRST-AB, 5, 014201 (2002). 7. Manuals to computer codes like TRACE3D, TRANSPORT, etc. Backup Slides

Detectors 24 mA, 10 keV, =0.9 Emittance (rms. Norm.) in DC Injection Exps.

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