xal.tools.beam.calc

Interface ISimulationResults.ISimEnvResults<S>

Type Parameters:

S - type of the probe state containing local simulation data

All Superinterfaces:

ISimulationResults

All Known Implementing Classes:

CalculationsOnBeams, CalculationsOnMachines, CalculationsOnRings, SimpleSimResultsAdaptor, SimResultsAdaptor

Enclosing interface:

ISimulationResults

public static interface ISimulationResults.ISimEnvResults<S>
extends ISimulationResults

Processes simulation data concerned with the beam properties.

For example, when S = xal.model.probe.traj.EnvelopeProbeState then the interface quantities are essentially beam parameters since the beam dynamics figure into the states of xal.model.probe.EnvelopeProbe.

Since:

2/9/05

Nested Class Summary

Nested classes/interfaces inherited from interface xal.tools.beam.calc.ISimulationResults

ISimulationResults.ISimEnvResults<S>, ISimulationResults.ISimLocResults<S>

Method Summary

Modifier and Type	Method and Description
R3	computeBetatronPhase(S state) Get the betatron phase values at the given state location for all three phase planes.
PhaseVector	computeChromDispersion(S state) Calculates the fixed point (closed orbit) in transverse phase space at the given state Sn location sn in the presence of dispersion.
Twiss[]	computeTwissParameters(S state) Returns the array of twiss objects for this state for all three planes at the location of the given simulation state.

Method Detail

computeTwissParameters

Twiss[] computeTwissParameters(S state)

Returns the array of twiss objects for this state for all three planes at the location of the given simulation state. These could be the matched beam Twiss parameters for a periodic structure or the dynamics Twiss parameters of a mismatched or otherwise evolving beam.

Parameters:

state - simulation state where Twiss parameters are computed

Returns:

array (twiss-H, twiss-V, twiss-L)

computeBetatronPhase

R3 computeBetatronPhase(S state)

Get the betatron phase values at the given state location for all three phase planes.

Parameters:

state - simulation state where parameters are computed

Returns:

vector (ψ_x, ψ_y, ψ_x) of phases in radians

computeChromDispersion

PhaseVector computeChromDispersion(S state)

Calculates the fixed point (closed orbit) in transverse phase space at the given state S_n location s_n in the presence of dispersion.

Let the full-turn map a the state location be denoted Φ_n (or the transfer matrix from entrance to location s_n for a linac). The transverse plane dispersion vector Δ is defined

Δ_t ≡ -(1/γ²)[dx/dz', dx'/dz', dy/dz', dy'/dz']^T .

It can be identified as the first 4 entries of the 6^th column in the transfer matrix Φ_n. The above vector quantifies the change in the transverse particle phase coordinate position versus the change in particle momentum. The factor -(1/γ²) is needed to convert from longitudinal divergence angle z' used by XAL to momentum δp ≡ Δp/p used in the dispersion definition. Specifically,

δp ≡ Δp/p = γ²z'

As such, the above vector can be better described

Δ_t ≡ [Δx/δp, Δx'/δp, Δy/δp, Δy'/δp]^T

explicitly describing the change in transverse phase coordinate for fractional change in momentum δp.

Since we are only concerned with transverse phase space coordinates, we restrict ourselves to the 4×4 upper diagonal block of Φ_n, which we denote take T_n. That is, T_n = π ⋅ Φ_n where π : R^6×6 → R^4×4 is the projection operator.

This method finds that point z_t ≡ (x_t, x'_t, y_t, y'_t) in transvse phase space that is invariant under the action of the ring for a given momentum spread δp. That is, the particle ends up in the same location each revolution. With a finite momentum spread of δp > 0 we require this require that

T_nz_t + δpΔ_t = z_t ,

which can be written

z_t = δp(T_n - I)^-1Δ_t ,

where I is the identity matrix. Dividing both sides by δp yields the final result

z₀ ≡ z_t/δp = (T_n - I)^-1Δ_t ,

which is the returned value of this method. It is normalized by δp so that we can compute the closed orbit for any given momentum spread.

Parameters:

state - we are calculating the dispersion at this state location

Returns:

The closed orbit fixed point z₀ for finite dispersion, normalized by momentum spread. Returned as an array [x₀,x'₀,y₀,y'₀]/δp

Since:

Nov 8, 2013