Twiss

java.lang.Object
- xal.tools.beam.Twiss

All Implemented Interfaces:

java.io.Serializable
```
public class Twiss
extends java.lang.Object
implements java.io.Serializable
```
Convenience class for dealing with Courant-Snyder (or Twiss) parameters. These parameters represent an ellipse in phase space given by

γx² + 2αxx' + βx'² = ε

where α, β, γ, and ε are the Courant-Snyder parameters and (x,x') are coordinates on the horizontal phase plane. (There are analogous equations for the other phase planes.) Recall that the Courant-Snyder parameters are not independent but related by the fact

βγ - α² = 1

Since:

Nov 12, 2002

See Also:

Serialized Form

Nested Class Summary

Nested Classes
Modifier and Type Class and Description

static class Twiss.PROP
Enumeration of the Courant-Snyder parameters used.

Nested Classes
Modifier and Type	Class and Description
`static class`	`Twiss.PROP` Enumeration of the Courant-Snyder parameters used.

Constructor Summary

Constructors
Constructor and Description
`Twiss()` Creates a new, uninitialized, instance of Twiss
`Twiss(double dblAlpha, double dblBeta, double dblEmitt)` Creates a new instance of Twiss initialized to the given Twiss parameters.
`Twiss(Twiss twiss)` Copy constructor: creates a deep copy of the argument.

Method Summary

All Methods Static Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`double[]`	`computeEigenvalues()` Compute and return the eigenvalues of the Twiss matrix.
`R2[]`	`computeEigenvectors()` Compute and return the eigenvectors of the Twiss matrix.
`double`	`computeRotation()` Compute the phase space ellipse's rotation from upright.
`double[]`	`computeSemiAxes()` Computes and returns the semi-axes of the phase space ellipse represented by the Twiss parameters.
`double[][]`	`correlationMatrix()` Return the correlation matrix associated with these Twiss parameters.
`static Twiss`	`createFromCovarianceMatrix(double[][] arrCov)` Create a new set of `Twiss` parameters from the given covariance matrix.
`static Twiss`	`createFromEquivalentBeam(double dblEnvRad, double dblEnvSlp, double dblEmit)` Creates a new `Twiss` object given the parameters of the equivalent uniform beam.
`static Twiss`	`createFromMoments(double dblMmtSigX, double dblMmtCov, double dblMmtSigXp)` Creates a new `Twiss` object initialized by the given set of central, second-order moments of the beam in whatever phase plane.
`double`	`getAlpha()` Return the alpha Twiss parameter
`double`	`getBeta()` Return the beta Twiss parameter
`double`	`getEmittance()` Return the beam emittance
`double`	`getEnvelopeRadius()` Return the envelope radius extent
`double`	`getEnvelopeSlope()` Return the envelope slope
`double`	`getGamma()` Return the gamma Twiss parameter
`void`	`printOn(java.io.PrintWriter pw)` Print out contents of the Twiss object.
`void`	`setEnvelope(double dblEnvRad, double dblEnvSlp, double dblEmitt)` Set the values of the Twiss parameters from the corresponding phase space envelope values.
`void`	`setTwiss(double dblAlpha, double dblBeta, double dblEmitt)` Sets the values of the Twiss parameters directly.
`java.lang.String`	`toString()` Get the twiss parameters as a string
`double[][]`	`twissMatrix()` Return the Twiss matrix associated with these Twiss parameters.

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Constructor Detail
  - Twiss
```
public Twiss()
```
    Creates a new, uninitialized, instance of Twiss
  - Twiss
```
public Twiss(Twiss twiss)
```
    Copy constructor: creates a deep copy of the argument.
    
    Parameters:
    
    twiss - twiss object to be copied.
  - Twiss
```
public Twiss(double dblAlpha,
             double dblBeta,
             double dblEmitt)
```
    Creates a new instance of Twiss initialized to the given Twiss parameters.
    
    Parameters:
    
    dblAlpha - coefficient of 2*x*x'
    
    dblBeta - coefficient of x'^2
    
    dblEmitt - magnitude^2 of the ellipse (beam emittance)
- Method Detail
  - createFromMoments
```
public static Twiss createFromMoments(double dblMmtSigX,
                                      double dblMmtCov,
                                      double dblMmtSigXp)
```
    Creates a new Twiss object initialized by the given set of central, second-order moments of the beam in whatever phase plane. Note that the RMS emittance ε is given by [<x²><x'²> - <xx'>²]^1/2For example, in the horizontal phase plane the parameters are given as
    
    Parameters:
    
    dblMmtSigX - the second moment <x²>
    
    dblMmtCov - the second moment <xx'>
    
    dblMmtSigXp - the second moment <x'²>
    
    Returns:
    
    the Courant-Snyder parameters (α=-<xx'>/ε, β=<x²>/ε, ε)
    
    Since:
    
    Aug 29, 2012
  - createFromCovarianceMatrix
```
public static Twiss createFromCovarianceMatrix(double[][] arrCov)
```
    Create a new set of Twiss parameters from the given covariance matrix. The covariance matrix is simply the second-order moments packaged up as a symmetric matrix. The form of this matrix σ is
```
     σ ≅ | <x²> <xx'> |
         | <xx'> <x'²> |
 
```
    Parameters:
    
    arrCov - symmetric matrix array of second-order moments
    
    Returns:
    
    Courant-Snyder parameters corresponding to the given covariance matrix
    
    Since:
    
    Aug 29, 2012
  - createFromEquivalentBeam
```
public static Twiss createFromEquivalentBeam(double dblEnvRad,
                                             double dblEnvSlp,
                                             double dblEmit)
```
    Creates a new Twiss object given the parameters of the equivalent uniform beam. This is the uniform beam that has the same second-moments as the beam under study. Because of the uniform charge distribution it can be modeled as a KV (Kapchinsky-Vladimirsky) beam having a distinct envelope size (radius) and a distinct envelope slope (this value is related to the divergence angle).
    
    NOTE
    · We do not scale the emittance! It is common practice to multiply the RMS emittance by 4 for 2D beams and other values for 3D beams with various distributions. We assume the same second moments which yield the same RMS emittance. Specially, the emittance of the returned object IS THE RMS EMITTANCE.
    
    Parameters:
    
    dblEnvRad - envelope size X of the uniform beam
    
    dblEnvSlp - slope divergence angle X' of the uniform beam
    
    dblEmit - emittance of the beam - This value is not scaled!
    
    Returns:
    
    Courant-Snyder parameters corresponding to the given equivalent uniform beam parameters
    
    Since:
    
    Aug 29, 2012
  - setTwiss
```
public void setTwiss(double dblAlpha,
                     double dblBeta,
                     double dblEmitt)
```
    Sets the values of the Twiss parameters directly.
    
    Parameters:
    
    dblAlpha - alpha parameter (phase plane coupling)
    
    dblBeta - beta parameter (the envelope magnitude)
    
    dblEmitt - beam emittance (phase space area)
  - setEnvelope
```
public void setEnvelope(double dblEnvRad,
                        double dblEnvSlp,
                        double dblEmitt)
```
    Set the values of the Twiss parameters from the corresponding phase space envelope values.
    
    Parameters:
    
    dblEnvRad - envelope radius
    
    dblEnvSlp - envelope slope
    
    dblEmitt - beam emittance
  - getAlpha
```
public double getAlpha()
```
    Return the alpha Twiss parameter
  - getBeta
```
public double getBeta()
```
    Return the beta Twiss parameter
  - getGamma
```
public double getGamma()
```
    Return the gamma Twiss parameter
  - getEmittance
```
public double getEmittance()
```
    Return the beam emittance
  - getEnvelopeRadius
```
public double getEnvelopeRadius()
```
    Return the envelope radius extent
  - getEnvelopeSlope
```
public double getEnvelopeSlope()
```
    Return the envelope slope
  - twissMatrix
```
public double[][] twissMatrix()
```
```
  Return the Twiss matrix associated with these Twiss parameters.
  This matrix has the form

      S = | gamma  alpha |
          | alpha  beta  |

  so that the equation of the phase space ellipse is given by

      (x,x')*S*(x,x') = emittance
 
```
    Returns:
    
    2x2 Twiss matrix
  - correlationMatrix
```
public double[][] correlationMatrix()
```
    Return the correlation matrix associated with these Twiss parameters.
    
    Returns:
    
    2x2 phase space correlation matrix
  - computeRotation
```
public double computeRotation()
```
    Compute the phase space ellipse's rotation from upright.
    
    Returns:
    
    phase space rotation (radians)
  - computeSemiAxes
```
public double[] computeSemiAxes()
```
```
  Computes and returns the semi-axes of the phase space ellipse
  represented by the Twiss parameters.  

  NOTE:
  Since the ellipse may be rotated these values do not necessarily
  correspond to any particular values of x, and x' in the phase plane.
 
```
    Returns:
    
    two-dimension array of semi-axes (a,b)
  - computeEigenvalues
```
public double[] computeEigenvalues()
```
```
  Compute and return the eigenvalues of the Twiss matrix.  This matrix has
  the form

          | gamma  alpha |
          | alpha  beta  |
          
 
```
    Returns:
    
    eigenvalues of the above matrix
  - computeEigenvectors
```
public R2[] computeEigenvectors()
```
```
  Compute and return the eigenvectors of the Twiss matrix.  This matrix has
  the form

          | gamma  alpha |
          | alpha  beta  |
          
 
```
    Returns:
    
    two-element array of eigenvectors of the above matrix
  - printOn
```
public void printOn(java.io.PrintWriter pw)
```
    Print out contents of the Twiss object.
    
    Parameters:
    
    pw - PrintWriter object to receive contents
  - toString
```
public java.lang.String toString()
```
    Get the twiss parameters as a string
    
    Overrides:
    
    toString in class java.lang.Object

Class Twiss

Nested Class Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

Twiss

Twiss

Twiss

Method Detail

createFromMoments

createFromCovarianceMatrix

createFromEquivalentBeam

NOTE

setTwiss

setEnvelope

getAlpha

getBeta

getGamma

getEmittance

getEnvelopeRadius

getEnvelopeSlope

twissMatrix

correlationMatrix

computeRotation

computeSemiAxes

computeEigenvalues

computeEigenvectors

printOn

toString