1 / 11

Emittance Calculation

1. Emittance Calculation. Chris Rogers, Imperial College/RAL Septemebr 2004. 2. Two Strands. G4MICE Analysis Code Calc 2/4/6D Emittance Apply statistical weights, cuts, etc Theory Phase Space/Geometric Emittance aren’t good for high emittance beams

felicia-pittman
Download Presentation

Emittance Calculation

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. 1 Emittance Calculation Chris Rogers, Imperial College/RAL Septemebr 2004

  2. 2 Two Strands • G4MICE Analysis Code • Calc 2/4/6D Emittance • Apply statistical weights, cuts, etc • Theory • Phase Space/Geometric Emittance aren’t good for high emittance beams • Looking at new ways to calculate emittance

  3. 3 Analysis Code Aims • For October Collaboration Meeting: • Plot emittance down the MICE Beamline • Trace space, phase space, canonical momenta • Enable tracker analysis • Apply statistical weights to events

  4. 4 Progress • Analysis Code can now • Calculate emittance • Apply statistical weights • Weight events such that they look Gaussian • Cut events that don’t make it to the downstream tracker, fall outside a certain pos/mom range • Still can’t do canonical coordinates

  5. 5 Class Diagram

  6. 6 Some Results Phase Space Emittances in constant Bz - Top left: 2D trans emittance. Top right: 2D long emittane. Bottom left: 4D trans emittance. Bottom right: 6D emittance

  7. 7 Theory • Emittance is not defined with highly dispersive beams in mind • Geometric emittance - calc’d using p/pz • Normalisation fails for non-symmetric highly dispersive beams • Phase Space Emittance - calc’d using p • Non-linear equations of motion => emittance increases in drift/solenoid • Looks like heating even though in drift space!

  8. 8 Solution? - 4D Hamiltonian • We can introduce a four dimensional Hamiltonian H=(Pu – Au)2/m • Pu is the canonical momentum 4-vector • Au is the 4 potential • Equations of motion are now linear in terms of the independent variable t given by t = ti/gi • Weird huh? Actually, this is in Goldstein Classical Mechanics. He points out that the “normal” Hamiltonian is not covariant, and not particularly relativistic.

  9. 9 Evolution in drift • The evolution in drift is now given by xu(t) = xu(0) + Put/m • This is linear so emittance is a constant • But proper time is not a physical observable • Need to do simulation work • Need to approach multiple scattering with caution • Stochastic process

  10. 10 Evolution in Fields • The Lorentz forces are Lorentz invariant so particle motion is still linear inside linear B-fields. That is dP/dt = q(dx/dt x B) • We can show this using more rigorous methods • This means that all of our old conditions for linear motion are still obeyed in the 4-space • However, in a time-varying field it is less clear how to deal with motion of a particle. • An RF cavity is sinusoidal in time - but what does it look like in proper time t? I don’t know…

  11. Summary • Analysis code coming along • Can apply statistical weights • Theory proving interesting • Need to look at RF, solenoids • Other avenues? Absolute density, etc • Other aspects (e.g. Holzer method)

More Related