IBSimu  1.0.4
Public Member Functions | Protected Attributes
Emittance Class Reference

Class for emittance statistics. More...

#include <trajectorydiagnostics.hpp>

Inheritance diagram for Emittance:
EmittanceConv

List of all members.

Public Member Functions

 Emittance ()
 Default constructor for emittance statistics.
 Emittance (const std::vector< double > &x, const std::vector< double > &xp, const std::vector< double > &I)
 Constructor for emittance statistics from trajectory diagnostic data columns x, xp and current I.
 Emittance (const std::vector< double > &x, const std::vector< double > &xp)
 Constructor for emittance statistics from trajectory diagnostic data columns x, xp, assuming even weights.
double xave (void)
double xpave (void)
double alpha (void)
double beta (void)
double gamma (void)
double epsilon (void)
double angle (void)
double rmajor (void)
double rminor (void)

Protected Attributes

double _Isum
double _xave
double _xpave
double _x2
double _xp2
double _xxp
double _alpha
double _beta
double _gamma
double _epsilon
double _angle
double _rmajor
double _rminor

Detailed Description

Class for emittance statistics.

Emittance class does a statistical analysis on the particle distribution and it calculates averages $ <x> $ and $ <x'> $ and the expectation values $ <x^2> $, $ <x'^2> $ and $ <x x'> $. From these it calculates the rms-emittance

\[ \epsilon = \sqrt{ <x^2><x'^2> - <x x'>^2 } \]

and the Twiss parameters

\[ \alpha = \frac{-<x x'>}{\epsilon}, \beta = \frac{<x^2>}{\epsilon}, \gamma = \frac{<x'^2>}{\epsilon} \]

In addition to these physical values, the class calculates the angle of the ellipse

\[ \theta = \frac{1}{2} \arctan{\left( \frac{2\alpha}{\beta - \gamma} \right)} \]

and the half-axis lengths

\[ r_1 = \sqrt{\frac{\epsilon}{2}} ( \sqrt{H+1} + \sqrt{H-1} ) \]

\[ r_2 = \sqrt{\frac{\epsilon}{2}} ( \sqrt{H+1} - \sqrt{H-1} ), \]

where

\[ H = \frac{\beta + \gamma}{2} \]


Constructor & Destructor Documentation

Emittance::Emittance ( )

Default constructor for emittance statistics.

Emittance::Emittance ( const std::vector< double > &  x,
const std::vector< double > &  xp,
const std::vector< double > &  I 
)

Constructor for emittance statistics from trajectory diagnostic data columns x, xp and current I.

Emittance::Emittance ( const std::vector< double > &  x,
const std::vector< double > &  xp 
)

Constructor for emittance statistics from trajectory diagnostic data columns x, xp, assuming even weights.


Member Function Documentation

double Emittance::alpha ( void  ) [inline]
double Emittance::angle ( void  ) [inline]
double Emittance::beta ( void  ) [inline]
double Emittance::epsilon ( void  ) [inline]
double Emittance::gamma ( void  ) [inline]
double Emittance::rmajor ( void  ) [inline]
double Emittance::rminor ( void  ) [inline]
double Emittance::xave ( void  ) [inline]
double Emittance::xpave ( void  ) [inline]

Member Data Documentation

double Emittance::_alpha [protected]
double Emittance::_angle [protected]
double Emittance::_beta [protected]
double Emittance::_epsilon [protected]
double Emittance::_gamma [protected]
double Emittance::_Isum [protected]
double Emittance::_rmajor [protected]
double Emittance::_rminor [protected]
double Emittance::_x2 [protected]
double Emittance::_xave [protected]
double Emittance::_xp2 [protected]
double Emittance::_xpave [protected]
double Emittance::_xxp [protected]

The documentation for this class was generated from the following file: