Package xal.tools.beam.optics

Class AcceleratingRfGap

java.lang.Object

xal.tools.beam.optics.AcceleratingRfGap

public class AcceleratingRfGap
extends Object

Class for modeling an accelerating RF gap as a thin lens.

Since:

Oct 1, 2015

Author:

Christopher K. Allen

Nested Class Summary

Nested Classes

Modifier and Type	Class	Description
static enum	AcceleratingRfGap.LOC	Enumeration specifying the upstream location or downstream locations for the RF accelerating gap.
static class	AcceleratingRfGap.NoConvergenceException	Class NoConvergenceException.

Constructor Summary

Constructors

Constructor	Description
AcceleratingRfGap(double f, double v0, AxialFieldSpectrum spcRfFld)	Initializing constructor for AcceleratingRfGap.

Method Summary

Modifier and Type	Method	Description
EnergyVector	computeGapGains(AcceleratingRfGap.LOC locHam, double q, double eR, EnergyVector vecInit)	Computes and returns the phase jump Δφ and energy gain ΔW imparted to a particle with the the given particle charge Q and rest energy Er for the given gap region.
double	computeNormWaveNumber(double w, double eR)	Compute and return the normalized wave number K.
EnergyVector	computePreGapGains(double eR, EnergyVector vecInit)	Deprecated.
double	getErrorTolerance()	Returns the maximum allowable error, the distance between iterates of (Δφ,ΔW), before the current iterate is considered a valid solution.
AxialFieldSpectrum	getFieldSpectrum()	Returns the spectrum of the gap's axial electric field.
int	getMaxIterations()	Returns the maximum number of allowable iterations during the iterative search for RF gap gain parameters Δφ and ΔW.
double	getRfFieldPotential()	Returns the total (integrated) potential gain of the RF field across the accelerating gap.
double	getRfFrequency()	Returns the time-harmonic frequency of gap accelerating field.
double	getRfWaveNumber()	Get the free space wave number k0 of the gap accelerating fields.
void	setErrorTolerance(double dblErrTol)	Sets the acceptable error tolerance when iterating for consistent gain parameters ΔW and Δφ.
void	setMaxIterations(int cntIterMax)	Set the maximum number of allowable iterations during a search for the consistent gain parameters Δφ and ΔW.
void	setRfFieldPotential(double v0)	Resets the total potential gain across the accelerating gap.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details

AcceleratingRfGap

public AcceleratingRfGap(double f,
 double v0,
 AxialFieldSpectrum spcRfFld)

Initializing constructor for AcceleratingRfGap. All parameters needed for defining the RF accelerating gap are provided.

Parameters:

f - time-harmonic frequency of the accelerating field (Hz)

v0 - total potential drop across gap axial field (Volts)

spcRfFld - spectrum of the RF field along design axis

Since:

Oct 1, 2015, Christopher K. Allen

Method Details

setMaxIterations

public void setMaxIterations(int cntIterMax)

Set the maximum number of allowable iterations during a search for the consistent gain parameters Δφ and ΔW. The default value for this quantity is given by the constant CNT_MAX_ITER.

Parameters:

cntIterMax - new value for maximum iteration count in gain computations

Since:

Oct 13, 2015, Christopher K. Allen

setErrorTolerance

public void setErrorTolerance(double dblErrTol)

Sets the acceptable error tolerance when iterating for consistent gain parameters ΔW and Δφ. The default value for this quantity is given by the constant DBL_ERR_TOL.

Parameters:

dblErrTol - new value for the error tolerance in gain computations

Since:

Oct 9, 2015, Christopher K. Allen

setRfFieldPotential

public void setRfFieldPotential(double v0)

Resets the total potential gain across the accelerating gap.

Parameters:

v0 - the integral ∫E_z(z) dz (in Volts)

Since:

Oct 16, 2015, Christopher K. Allen

getMaxIterations

public int getMaxIterations()

Returns the maximum number of allowable iterations during the iterative search for RF gap gain parameters Δφ and ΔW.

Returns:

maximum iteration count in (Δφ,ΔW) phase jump, energy gain computations

Since:

Oct 13, 2015, Christopher K. Allen

See Also:

• AcceleratingRfGap#setMaxIterations()

getErrorTolerance

public double getErrorTolerance()

Returns the maximum allowable error, the distance between iterates of (Δφ,ΔW), before the current iterate is considered a valid solution. Once the L₂ distance between the current iterate of phase jump Δφ and energy gain ΔW and the previous iterate is less than this value, then the iteration stops with a valid solution.

Returns:

maximum distance between solution iterations for valid solution

Since:

Oct 13, 2015, Christopher K. Allen

getRfFrequency

public double getRfFrequency()

Returns the time-harmonic frequency of gap accelerating field.

Returns:

the RF frequency of the electric field (Hz)

Since:

Sep 28, 2015 by Christopher K. Allen

getRfWaveNumber

public double getRfWaveNumber()

Get the free space wave number k₀ of the gap accelerating fields. This quantity has the formula

k₀ = 2π/λ

where λ = c/f is the wave length of the RF in free space.

Returns:

free space wave number k₀ of gap RF

Since:

Oct 1, 2015, Christopher K. Allen

getRfFieldPotential

public double getRfFieldPotential()

Returns the total (integrated) potential gain of the RF field across the accelerating gap. This is the value given by

V₀ ≜ ∫E_z(0,z)dz ,

where the integral is taken over the entire real line z ∈ (-∞,+∞). This value represents the total available accelerating RF energy and an upper limit for energy gain.

Returns:

the total potential V₀ across the accelerating gap (in Volts)

Since:

Oct 2, 2015, Christopher K. Allen

getFieldSpectrum

public AxialFieldSpectrum getFieldSpectrum()

Returns the spectrum of the gap's axial electric field.

Returns:

spectrum object describing the electric field along the gap axis

Since:

Oct 9, 2015, Christopher K. Allen

computeGapGains

public EnergyVector computeGapGains(AcceleratingRfGap.LOC locHam,
 double q,
 double eR,
 EnergyVector vecInit)
                             throws AcceleratingRfGap.NoConvergenceException

Computes and returns the phase jump Δφ and energy gain ΔW imparted to a particle with the the given particle charge Q and rest energy E_r for the given gap region. The particle enters this region with initial gap phase φ₀ and initial kinetic energy W_i. The returned values represent the effects of the first have of this gap upon the so described particle. This method uses an iterative technique to compute the results in order to maintain a self-consistent set of expressions. That is, the modeling expressions are a set of transcendental equations which must be solved self-consistently. Thus, we are relegated to iterative methods.

The provided phase φ₀ is assumed to be the phase of the particle at the center of the gap, if it were coasting through the gap with kinetic energy W_i for the pre-gap computation, and after the pre-gap phase jump Δφ^- for the post-gap computation. The phase value returned by this method, either Δφ^- or Δφ⁺ for the pre-gap or post-gap calculation, respectively, is

Δφ^- = +φ₀ - φ₀^- ,
Δφ⁺ = -φ₀ + φ₀⁺ ,

where φ₀^- is the thin-lens model gap center intercept of the incoming coasting particle, φ₀⁺ is the thin-lens model gap center intercept of the outgoing coasting particle, and φ₀ is the actual particle phase at the gap center. The total phase jump at the gap center Δφ is the sum of these two phase jumps,

Δφ = Δφ^- + Δφ⁺ = φ₀⁺ - φ₀^- ,

The returned energy gain, either ΔW^- for the pre-gap location or ΔW⁺ for the post-gap location, is the energy gained by the particle in those respective locations. The total energy gained by a particle through the gap is the sum of these energies

ΔW = ΔW^- + ΔW⁺ .

Parameters:

locHam - location of longitudinal gain calculations, with respect to gap center

q - charge of the incoming particles in terms of fundamental charge q (unitless)

eR - rest energy of the incoming particles (electron-Volts)

vecInit - initial phase and energy pair (φ₀,W_i) into specified gap region (radians, electron-Volts)

Returns:

the corrective phase jump and energy gain pair (Δφ,ΔW) after impulse at specified location, pre- or post-gap (radians, electron-Volts)

Throws:

AcceleratingRfGap.NoConvergenceException - the iterative search for (Δφ,ΔW) failed to converge

Since:

Oct 15, 2015, Christopher K. Allen

computePreGapGains

@Deprecated
public EnergyVector computePreGapGains(double eR,
 EnergyVector vecInit)
                                throws AcceleratingRfGap.NoConvergenceException

Deprecated.

Computes and returns the phase jump Δφ and energy gain ΔW imparted to a particle with the the given rest energy E_r, gap phase φ₀^-, and initial kinetic energy W_i. The returned values represent the effects of the first have of this gap upon the so described particle. This method uses an iterative technique to compute the results in order to maintain a self-consistent set of expressions. That is, the modeling expressions are a set of transcendental equations which must be solved self-consistently. Thus, we are relegated to iterative methods.

The provided phase φ₀^- is assumed to be the phase of the particle at the center of the gap if it were coasting through the gap with kinetic energy W_i. The actual phase at the gap center φ₀ will be

φ₀ = φ₀^- + Δφ ,

where Δφ is the phase jump returned by this method.

The returned energy gain ΔW is that for the particle at the gap center. That is, the effects of the gap on the particle include an energy gain of ΔW up to the gap center. The total kinetic energy W₀ at gap center is then

W₀ = W_i + ΔW.

Parameters:

eR - rest energy of the incoming particles (electron-Volts)

vecInit - gap phase and initial energy pair (φ₀^-,W_i) (radians, electron-Volts)

Returns:

the corrective phase jump and energy gain pair (Δφ,ΔW) at gap center (radians, electron-Volts)

Throws:

AcceleratingRfGap.NoConvergenceException - the iterative search for (Δφ,ΔW) failed to converge

Since:

Oct 15, 2015, Christopher K. Allen

computeNormWaveNumber

public double computeNormWaveNumber(double w,
 double eR)

Compute and return the normalized wave number K. This quantity appears as a constant in the phase jump expressions. The value of K is defined by the formula

K ≜ (1/β³γ³) (qV₀/mc²)k₀

where β is the normalized particle velocity, γ is the relativistic factor; V₀ is the total (integrated) RF field potential across the gap, mc²/q is the rest mass in electron-Volts, and k₀ ≜ 2π/λ is the free-space wave number of the accelerating RF field with wavelength λ.

The quantity K can be interpreted as the particle wave number in energy space rather that momentum space.

Parameters:

w - particle kinetic energy W (electron-Volts)

eR - particle rest mass mc²/q (electron-Volts)

Returns:

normalized wave number K (in radians/meter)

Since:

Oct 1, 2015, Christopher K. Allen