#include <Hamiltonian.h>

Collaboration diagram for Hamiltonian:

Public Types
typedef FTps< double, 6 >	series_t

Public Member Functions
	Hamiltonian (int truncOrder)

Hamiltonian::series_t	drift (const double &gamma0)

Hamiltonian::series_t	rbend (double &beta0, double &gamma0, double &q, double &h, double &K0)

Hamiltonian::series_t	sbend (const double &gamma0, const double &h, const double &k0)

Hamiltonian::series_t	bendFringe (double &beta0, double &gamma0, double &h, double &k0, series_t &ax, series_t &az)

Hamiltonian::series_t	quadrupole (const double &gamma0, const double &q, const double &k1)

Hamiltonian::series_t	fringeField (const double &phi, const double &k0)

Public Attributes
series_t	x

series_t	px

series_t	y

series_t	py

series_t	z

series_t	delta

Detailed Description

Definition at line 19 of file Hamiltonian.h.

Member Typedef Documentation

typedef FTps<double, 6 > Hamiltonian::series_t

Definition at line 23 of file Hamiltonian.h.

Constructor & Destructor Documentation

Hamiltonian::Hamiltonian ( int truncOrder )

explicit

Definition at line 3 of file Hamiltonian.cpp.

References delta, FTps< double, 6 >::makeVariable(), px, py, FTps< double, 6 >::setGlobalTruncOrder(), x, y, and z.

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Member Function Documentation

Hamiltonian::series_t Hamiltonian::bendFringe	(	double &	beta0,
		double &	gamma0,
		double &	h,
		double &	k0,
		series_t &	ax,
		series_t &	az
	)

:TODO: WIP: Fringe Field SBend

\[H_{Dipole}= \frac{\delta}{\beta_0} - \left( 1+ hx \right) \sqrt{\left(\frac{1}{\beta_0} + \delta \right)^2 -(p_x - a_x)^2 -p_y^2 - \frac{1}{\left(\beta_0 \gamma_0\right)^2 } } + \left( 1+ hx \right) k_0 \left(x - \frac{hx^2}{2 \left( 1+ hx \right)}\right) \]

Parameters

beta0
gamma0	Lorenz factor
k0	normalized magnetic field ( \( k0 = \frac{B q}{P_0}\), where \(q\) is the particle charge and \(P_0\) the momentum of the reference particle)
ax	Vector potential in x
az	longitudinal vector potential (in z)

Definition at line 77 of file Hamiltonian.cpp.

References delta, px, py, and sqrt().

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Hamiltonian::series_t Hamiltonian::drift ( const double & gamma0 )

Drift Space Hamiltonian

\[ H_{Drift}= \frac{\delta}{\beta_0} - \sqrt{\left(\frac{1}{\beta_0} + \delta \right)^2 -p_x^2 -p_y^2 - \frac{1}{\left(\beta_0 \gamma_0\right)^2 } } \]

Parameters

gamma0 Lorenz factor

Definition at line 16 of file Hamiltonian.cpp.

References delta, px, py, and sqrt().

Referenced by ThickTracker::fillGaps_m(), and ThickTracker::visitDrift().

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Hamiltonian::series_t Hamiltonian::fringeField	(	const double &	phi,
		const double &	k0
	)

Hamiltonian for a linear Thin Lens fringe field approximation

\[ H_{ThinLens} = \frac{1}{2} (x^2 - y^2) k_0 \tan \left( \Psi \right) \]

Parameters

phi	pole face roation angle
k0	normalized magnetic field ( \( k0 = \frac{B q}{P_0}\), where \(q\) is the particle charge and \(P_0\) the momentum of the reference particle)

Definition at line 132 of file Hamiltonian.cpp.

References tan(), x, and y.

Referenced by ThickTracker::visitSBend().

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Hamiltonian::series_t Hamiltonian::quadrupole	(	const double &	gamma0,
		const double &	q,
		const double &	k1
	)

Quadrupole Hamiltonian

\[ H_{Quadrupole}= \frac{\delta}{\beta_0} - \sqrt{\left(\frac{1}{\beta_0} + \delta \right)^2 -p_x^2 -p_y^2 - \frac{1}{\left(\beta_0 \gamma_0\right)^2 } } + \frac{1}{2} k_1 \left( x^2 - y^2 \right) \]

Parameters

gamma0	Lorenz factor
q	particle charge
k1	normalised field gradient ( \( k1 = \frac{B q}{P_0 r_0}\), where \(q\) is the particle charge, \(P_0\) the momentum of the reference particle and \(r_0\) the element aperture)

Definition at line 116 of file Hamiltonian.cpp.

References delta, px, py, sqrt(), x, and y.

Referenced by ThickTracker::visitMultipole().

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Hamiltonian::series_t Hamiltonian::rbend	(	double &	beta0,
		double &	gamma0,
		double &	q,
		double &	h,
		double &	K0
	)

:TODO: WIP:Rectangular Bend Hamiltonian

\[ H_{Dipole}= \frac{\delta}{\beta_0} - \left( 1+ hx \right) \sqrt{\left(\frac{1}{\beta_0} + \delta \right)^2 -p_x^2 -p_y^2 - \frac{1}{\left(\beta_0 \gamma_0\right)^2 } } + \left( 1+ hx \right) k_0 \left(x - \frac{hx^2}{2 \left( 1+ hx \right)}\right) \]

Definition at line 28 of file Hamiltonian.cpp.

References delta, px, py, sqrt(), and x.

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Hamiltonian::series_t Hamiltonian::sbend	(	const double &	gamma0,
		const double &	h,
		const double &	k0
	)

Sector Bend Hamiltonian

\[ H_{DipoleFringeField}= \frac{\delta}{\beta_0} - \left( 1+ hx \right) \sqrt{\left(\frac{1}{\beta_0} + \delta \right)^2 -\left( p_x - \frac{1}{2} \frac{k_0}{l} \left( s^2 - y^2 \right) \right) ^2 -p_y^2 - \frac{1}{\left(\beta_0 \gamma_0\right)^2 } } + \left( 1+ hx \right) \frac{1}{2} \frac{k_0}{l} \left( y^2 - x^2 \right) \tan \left( \Psi \right) \]

Parameters

gamma0	Lorenz factor
h	curvature ( \( \frac{1}{R} \) , where \( R \) is the bend radius)
k0	normalized magnetic field ( \( k0 = \frac{B q}{P_0}\), where \(q\) is the particle charge and \(P_0\) the momentum of the reference particle)

Definition at line 55 of file Hamiltonian.cpp.

References delta, px, py, sqrt(), and x.

Referenced by ThickTracker::visitSBend().

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