1 / 20

Emittance and Emittance Measurements S. Bernal

Emittance and Emittance Measurements S. Bernal. USPAS 08 U. of Maryland, College Park. Introduction: Phase and Trace Spaces, Liouville’s theorem, etc. IREAP. Vlasov Approx. G -Space. m -Space. 6N dim. 6 dim. p X →. Trace Space. Matrix notation:. or. Liouville’s Theorem :

stevenperez
Télécharger la présentation

Emittance and Emittance Measurements S. Bernal

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Emittance and Emittance MeasurementsS. Bernal USPAS 08 U. of Maryland, College Park

  2. Introduction: Phase and Trace Spaces, Liouville’s theorem, etc. IREAP Vlasov Approx. G-Space m-Space 6N dim. 6 dim. pX→ Trace Space Matrix notation: or Liouville’s Theorem: area conserved in either G or m spaces for 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).

  3. IREAP Transverse coordinate for paraxial particle motion in linear lattice obeys : Further, a, b, g: Courant-Snyder or Twiss Parameters. Review of Courant-Snyder Theory b(s)is a lattice function that depends on k0 (s), but A and φare different for different particles. The ellipse equation defines self-similar ellipses of area pAX2at a given plane s. Thelargest ellipse defines the beam emittance through

  4. IREAP a0: zero-current 2rms beam radius Space charge and emittance (M. Reiser, Chap. 5) If linear space charge is included, then k0(s)→k(s)and the b function is no longer just a lattice function because it now depends on current also. b becomes a lattice+beam function. Further, adding space charge does not require changing the emittance definition…Emittance and current are independent parameters in the envelope equation: The emittance above is the effective or 4rms emittance (also called edge emittance) which is equal to the total (100%) emittance for a K-V distribution. For a Gaussian distribution, the total and RMS emittances are equal when the Gaussian is truncated at 1-s.

  5. IREAP Linear system: Define: RMS Emittance and Envelope Equation(Pat G. O’Shea)

  6. IREAP Without acceleration, rms emittance of a mono-energetic beam is conserved under linear forces (both external and internal): X’ X’ x x X’ X’ x x Emittance Growth (M. Reiser, Chap. 6) The normalized emittance is an invariant: If initial transverse beam distribution is not uniform, 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.

  7. IREAP Laminar and Turbulent Flows

  8. IREAP Transverse Emittance Measurement Techniques

  9. IREAP By focusing a beam with a lens and measuring the width at a fixed distance z=L downstream from the lens, one can determine the emittance. Without space charge we have: slope radius R0 R(L) We find: Z Z=L Z=0 Basic Optics I

  10. IREAP Beam free expansion with space charge: emittance can be determined as a fit parameter in envelope calculation. 1 cm Z = 1.28 cm Additional beam optics checks possible with solenoid and quadrupole focusing. Z = 3.83 cm Z = 6.38 cm Z = 8.88 cm Z = 11.28 cm Basic Optics II

  11. IREAP Pepper-Pot Technique

  12. IREAP (b) (a) 0.166 mm/pixel (c) Pepper-Pot Technique 10keV, 100 mA, 700 experiment X = 67 μm, Y = 55 μm

  13. IREAP Pepper-Pot Technique Calculating emittance and plotting phase space:

  14. IREAP So beam ellipse can be written as The condition bg-a2=1iswritten Beam (s)and Transfer (R) Matrices Define the beam matrix for, say, x-plane: Consider 2 planes z0 and z1, z1>z0. Particle coordinates transform as: R is the Transfer matrix. Then, the beam matrix is transformed according to:

  15. IREAP d Solenoid IC2 Q2 IC1 Quadrupole Scan

  16. IREAP Quadrupole Scan: results for 6 mA beam

  17. References • Martin Reiser, Theory and Design of Charged-Particle Beams, 2nd Ed, Secs. 3.8.2, 5.3.4 (see Table 5.1) and Chapter 6. 2 D. A. Edwards and M. J. Syphers, An Introduction to the Physics of High Energy Accelerators, Sec. 3.2.4 (see Table 3.1). • Claude Lejeune and Jean Aubert, Emittance and Brightness: Definitions and Measurements, Advances in Electronics and 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 for Accelerator Applications, AIP Conf. Proc. No. 253; M.J. Rhee, Phys. Fluids 29 (1986). • Michiko G. Minty and Frank Zimmermann, Beam Techniques, Beam Control and Manipulation, USPAS, 1999. 6. S. G. Anderson, J. B. Rosenzweig, G. P. LeSage, and 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. .

  18. IREAP Backup Slides

  19. IREAP Detectors

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

More Related