# Emittance in addition to Emittance Measurements S. Bernal Basic Optics I Basic Optics II Pepper-Pot Technique Pepper-Pot Technique

## Emittance in addition to Emittance Measurements S. Bernal Basic Optics I Basic Optics II Pepper-Pot Technique Pepper-Pot Technique

Go, Rebecca, 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, Liouvilles theorem, etc. Liouvilles 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. OShea) 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