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* Definition of Lorene class Et_rot_mag
*
*/
/*
* Copyright (c) 2002 Emmanuel Marcq
* Copyright (c) 2002,2013 Jerome Novak
* Copyright (c) 2013 Deberati Chatterjee
*
* This file is part of LORENE.
*
* LORENE is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* LORENE is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with LORENE; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
#ifndef __ET_ROT_MAG_H_
#define __ET_ROT_MAG_H_
/*
* $Id: et_rot_mag.h,v 1.26 2015/06/12 12:38:24 j_novak Exp $
* $Log: et_rot_mag.h,v $
* Revision 1.26 2015/06/12 12:38:24 j_novak
* Implementation of the corrected formula for the quadrupole momentum.
*
* Revision 1.25 2014/10/21 09:23:53 j_novak
* Addition of global functions mass_g(), angu_mom(), grv2/3() and mom_quad().
*
* Revision 1.24 2014/10/13 08:52:34 j_novak
* Lorene classes and functions now belong to the namespace Lorene.
*
* Revision 1.23 2014/05/27 12:32:28 j_novak
* Added possibility to converge to a given magnetic moment.
*
* Revision 1.22 2014/05/13 10:06:12 j_novak
* Change of magnetic units, to make the Lorene unit system coherent. Magnetic field is now expressed in Lorene units. Improvement on the comments on units.
*
* Revision 1.21 2014/04/29 13:46:06 j_novak
* Addition of switches 'use_B_in_eos' and 'include_magnetisation' to control the model.
*
* Revision 1.20 2014/04/28 12:48:12 j_novak
* Minor modifications.
*
* Revision 1.19 2013/12/13 16:36:51 j_novak
* Addition and computation of magnetisation terms in the Einstein equations.
*
* Revision 1.18 2013/11/25 13:52:11 j_novak
* New class Et_magnetisation to include magnetization terms in the stress energy tensor.
*
* Revision 1.17 2012/08/12 17:48:36 p_cerda
* Magnetstar: New classes for magnetstar. Allowing for non-equatorial symmetry in Etoile et al. Adding B_phi in Et_rot_mag.
*
* Revision 1.16 2011/10/06 14:55:36 j_novak
* equation_of_state() is now virtual to be able to call to the magnetized
* Eos_mag.
*
* Revision 1.15 2005/06/02 11:35:27 j_novak
* Added members for sving to a file and reading from it.
*
* Revision 1.14 2004/03/22 13:12:41 j_novak
* Modification of comments to use doxygen instead of doc++
*
* Revision 1.13 2002/10/11 11:47:35 j_novak
* Et_rot_mag::MHD_comput is now virtual.
* Use of standard constructor for Tenseur mtmp in Et_rot_mag::equilibrium_mag
*
* Revision 1.12 2002/10/09 07:54:29 j_novak
* Et_rot_bifluid and Et_rot_mag inheritate virtually from Etoile_rot
*
* Revision 1.11 2002/08/02 15:07:41 j_novak
* Member function determinant has been added to the class Metrique.
* A better handling of spectral bases is now implemented for the class Tenseur.
*
* Revision 1.10 2002/06/05 15:15:59 j_novak
* The case of non-adapted mapping is treated.
* parmag.d and parrot.d have been merged.
*
* Revision 1.9 2002/06/03 13:23:16 j_novak
* The case when the mapping is not adapted is now treated
*
* Revision 1.8 2002/06/03 13:00:45 e_marcq
*
* conduc parameter read in parmag.d
*
* Revision 1.7 2002/05/30 16:06:30 j_novak
* added the right et_rot_mag.h
*
* Revision 1.6 2002/05/20 08:27:59 j_novak
* *** empty log message ***
*
* Revision 1.5 2002/05/17 15:08:01 e_marcq
*
* Rotation progressive plug-in, units corrected, Q and a_j new member data
*
* Revision 1.4 2002/05/15 09:53:59 j_novak
* First operational version
*
* Revision 1.3 2002/05/14 13:38:36 e_marcq
*
*
* Unit update, new outputs
*
* Revision 1.1 2002/05/10 09:26:51 j_novak
* Added new class Et_rot_mag for magnetized rotating neutron stars (under development)
*
*
* $Header: /cvsroot/Lorene/C++/Include/et_rot_mag.h,v 1.26 2015/06/12 12:38:24 j_novak Exp $
*
*/
// Headers Lorene
#include "etoile.h"
#include "tensor.h"
namespace Lorene {
// Local prototype (for determining the surface)
Cmp prolonge_c1(const Cmp& uu, const int nzet) ;
/**
* Class for magnetized (isolator or perfect conductor),
* rigidly rotating stars. \ingroup (star)
*
* This is a child class of \c Etoile_rot , with the same metric
* and overloaded member functions. Triaxial pertubrations are not
* operational.
*
*/
class Et_rot_mag : public Etoile_rot {
// Data :
// -----
protected:
///t-component of the elecctromagnetic potential 1-form, divided by \f$\mu_0\f$.
Cmp A_t ;
/**
* \f$\varphi\f$-component of the electromagnetic potential 1-form
* divided by \f$\mu_0\f$.
*/
Cmp A_phi;
Cmp B_phi; ///< \f$\varphi\f$-component of the magnetic field
Cmp j_t; ///< t-component of the current 4-vector
Cmp j_phi; ///< \f$\varphi\f$-component of the current 4-vector
Tenseur E_em; ///< electromagnetic energy density in the Eulerian frame
/**
* \f$\varphi\f$ component of the electromagnetic momentum density 3-vector,
* as measured in the Eulerian frame.
*/
Tenseur Jp_em;
///rr component of the electromagnetic stress 3-tensor, as measured in the Eulerian frame. (not used and set to 0, should be supressed)
Tenseur Srr_em;
///\f$\varphi \varphi\f$ component of the electromagnetic stress 3-tensor, as measured in the Eulerian frame.
Tenseur Spp_em;
/**
* In the case of a perfect conductor, the requated baryonic charge.
* For an isolator, the charge/baryon.
*/
double Q ;
double a_j ; ///<Amplitude of the curent/charge function
int conduc ; ///<Flag: conduc=0->isolator, 1->perfect conductor
// Constructors - Destructor
// -------------------------
public:
/// Standard constructor
Et_rot_mag(Map& mp_i, int nzet_i, bool relat, const Eos& eos_i,
const int cond);
Et_rot_mag(const Et_rot_mag& ) ; ///< Copy constructor
/** Constructor from a file (see \c sauve(FILE*) ).
*
* @param mp_i Mapping on which the star will be defined
* @param eos_i Equation of state of the stellar matter
* @param fich input file (must have been created by the function
* \c sauve )
* @param withbphi flag to create classes with toroidal field
*/
Et_rot_mag(Map& mp_i, const Eos& eos_i, FILE* fich, int withbphi=0) ;
virtual ~Et_rot_mag() ; ///< Destructor
// Memory management
// -----------------
protected:
/// Deletes all the derived quantities
virtual void del_deriv() const ;
/// Sets to \c 0x0 all the pointers on derived quantities
virtual void set_der_0x0() const ;
/** Sets to \c ETATNONDEF (undefined state) the hydrodynamical
* quantities relative to the Eulerian observer.
*/
virtual void del_hydro_euler() ;
// Mutators / assignment
// ---------------------
public:
/// Assignment to another Et_rot_mag
void operator=(const Et_rot_mag&) ;
/* /\** Computes the proper baryon and energy density, as well as */
/* * pressure from the enthalpy. */
/* *\/ */
/* virtual void equation_of_state() ; */
// Accessors
// ---------
public:
/// Tells if the star is made of conducting or isolating material
bool is_conduct() const {return (conduc==1) ;} ;
/**
* Returns the t component of the electromagnetic potential,
* divided by \f$\mu_0\f$.
*/
const Cmp& get_At() const {return A_t ; } ;
/**
* Returns the \f$\varphi\f$ component of the electromagnetic potential
* divided by \f$\mu_0\f$.
*/
const Cmp& get_Aphi() const {return A_phi ;} ;
///Returns the \f$\varphi\f$ component of the magnetic field
const Cmp& get_Bphi() const {return B_phi ;} ;
///Returns the t component of the current 4-vector
const Cmp& get_jt() const {return j_t ; } ;
///Returns the \f$\varphi\f$ component of the current 4-vector
const Cmp& get_jphi() const {return j_phi ;} ;
///Returns the electromagnetic energy density in the Eulerian frame
const Tenseur& get_Eem() const {return E_em ; } ;
/** Returns the \f$\varphi\f$-component of the electromagnetic momentum
* density 3-vector, as measured in the Eulerian frame.
*/
const Tenseur& get_Jpem() const {return Jp_em ;} ;
/** Returns the rr-component of the electromagnetic stress 3-tensor,
* as measured in the Eulerian frame. (not used and always equal to 0,
* should be supressed)
*/
const Tenseur& get_Srrem() const {return Srr_em ; } ;
/** Returns the \f$\varphi \varphi\f$ component of the electromagnetic
* stress 3-tensor, as measured in the Eulerian frame.
*/
const Tenseur& get_Sppem() const {return Spp_em ;} ;
/**
* Returns the requested electric charge in the case of a perfect conductor
* and the charge/baryon for an isolator.
*/
double get_Q() const {return Q ;} ;
///Returns the amplitude of the current/charge function
double get_a_j() const {return a_j ;} ;
// Outputs
// -------
public:
virtual void sauve(FILE* ) const ; ///< Save in a file
/// Operator >> (virtual function called by the operator <<).
virtual ostream& operator>>(ostream& ) const ;
// Global quantities
// -----------------
public:
/// Computes the electric field spherical components in Lorene's units
Tenseur Elec() const ;
/// Computes the magnetic field spherical components in Lorene's units
Tenseur Magn() const ;
/// Computes the electromagnetic part of the stress-energy tensor
virtual void MHD_comput() ;
virtual double mass_g() const ; ///< Gravitational mass
virtual double angu_mom() const ; ///< Angular momentum
virtual double grv2() const ; ///< Error on the virial identity GRV2
virtual double tsw() const ; ///< Ratio T/W
double MagMom() const ; ///< Magnetic Momentum \f$\cal M\f$ in SI units
/// Computed charge deduced from the asymptotic behaviour of At [SI units].
double Q_comput() const;
/** Computed charge from the integration of charge density over the star
* (i.e. without surface charge) [SI units].
*/
double Q_int() const;
/// Gyromagnetic ratio \f$\sigma = \frac{2{\cal M}M}{QJ}\f$.
double GyroMag() const ;
/** Error on the virial identity GRV3.
* The error is computed as the integral defined
* by Eq. (43) of [Gourgoulhon and Bonazzola,
* \a Class. \a Quantum \a Grav. \b 11 , 443 (1994)] divided by
* the integral of the matter terms.
*
* @param ost output stream to give details of the computation;
* if set to 0x0 [default value], no details will be
* given.
*
*/
virtual double grv3(ostream* ost = 0x0) const ;
/** Part of the quadrupole moment.
* This term \f${\bar Q }\f$ is defined by Laarakkers and Poisson,
* \a Astrophys. \a J. \b 512 , 282 (1999). Note that \f${\bar Q }\f$
* is the negative of the (wrong) quadrupole moment defined in Eq. (7) of
* [Salgado, Bonazzola, Gourgoulhon and Haensel, \a Astron. \a Astrophys.
* \b 291 , 155 (1994)].
*/
virtual double mom_quad_old() const ;
// Computational routines
// ----------------------
public:
/** Computes the electromagnetic quantities solving the Maxwell
* equations (6) and (7) of [Bocquet, Bonazzola, Gourgoulhon and
* Novak, \a Astron. \a Astrophys. \b 301 , 757 (1995)]. In the case
* of a perfect conductor, le electromagnetic potential may have
* a discontinuous derivative across star's surface.
*
* @param conduc [input] flag: 0 for an isolator, 1 for a perfect
* conductor
* @param adapt_flag [input] flag: if 0 the mapping is NOT adapted
* to star's surface
* @param f_j [input] current or charge coupling function
* (see Bocquet et al. 1995).
* @param par_poisson_At [input] parameters for controlling the
* solution of the Poisson equation
* for At potential (see file
* et_rot_mag_equil.C)
* @param par_poisson_Avect [input] parameters for controlling the
* solution of vector Poisson equation
* for magnetic potential (see file
* et_rot_mag_equil.C)
*/
void magnet_comput(const int adapt_flag,
Cmp (*f_j)(const Cmp& x, const double),
Param& par_poisson_At, Param& par_poisson_Avect) ;
/** Computes the electromagnetic quantities solving the Maxwell
* equations (6) and (7) of [Bocquet, Bonazzola, Gourgoulhon and
* Novak, \a Astron. \a Astrophys. \b 301 , 757 (1995)]. In the case
* of a perfect conductor, le electromagnetic potential may have
* a discontinuous derivative across star's surface.
*
* @param adapt_flag [input] flag: if 0 the mapping is NOT adapted
* to star's surface
* @param initial_j [input] flag: initial current for the iteration:
* 0= no current, 1=dipolar-like current
* , 2= quadrupolar-like current
* @param a_j0 [input] amplitude of the non-force free current
* @param f_j [input] current coupling function (non-FF part)
* (see Bocquet et al. 1995).
* @param b_j0 [input] amplitude of the force free current
* @param g_j [input] current coupling function (FF-part)
* @param N_j [input] current coupling function (FF-part)
* @param par_poisson_At [input] parameters for controlling the
* solution of the Poisson equation
* for At potential (see file
* et_rot_mag_equil.C)
* @param par_poisson_Avect [input] parameters for controlling the
* solution of vector Poisson equation
* for magnetic potential (see file
* et_rot_mag_equil.C)
*/
virtual void magnet_comput_plus(const int adapt_flag, const int initial_j,
const Tbl an_j,
Cmp (*f_j)(const Cmp& x, const Tbl),
const Tbl bn_j,
Cmp (*g_j)(const Cmp& x, const Tbl),
Cmp (*N_j)(const Cmp& x, const Tbl),
Param& par_poisson_At, Param& par_poisson_Avect) ;
/** Computes an equilibrium configuration.
*
* @param ent_c [input] Central enthalpy
* @param omega0 [input] Requested angular velocity
* (if \c fact_omega=1. )
* @param fact_omega [input] 1.01 = search for the Keplerian frequency,
* 1. = otherwise.
* @param nzadapt [input] Number of (inner) domains where the mapping
* adaptation to an iso-enthalpy surface
* should be performed
* @param ent_limit [input] 1-D \c Tbl of dimension \c nzet which
* defines the enthalpy at the outer boundary
* of each domain
* @param icontrol [input] Set of integer parameters (stored as a
* 1-D \c Itbl of size 8) to control the
* iteration:
* \li \c icontrol(0) = mer_max : maximum number of steps
* \li \c icontrol(1) = mer_rot : step at which the rotation is
* switched on
* \li \c icontrol(2) = mer_change_omega : step at which the rotation
* velocity is changed to reach the final one
* \li \c icontrol(3) = mer_fix_omega : step at which the final
* rotation velocity must have been reached
* \li \c icontrol(4) = mer_mass : the absolute value of
* \c mer_mass is the step from which the
* baryon mass is forced to converge,
* by varying the central enthalpy
* (\c mer_mass > 0 ) or the angular
* velocity (\c mer_mass < 0 )
* \li \c icontrol(5) = mermax_poisson : maximum number of steps in
* \c Map_et::poisson
* \li \c icontrol(6) = mer_triax : step at which the 3-D
* perturbation is switched on
* \li \c icontrol(7) = delta_mer_kep : number of steps
* after \c mer_fix_omega when \c omega
* starts to be increased by \c fact_omega
* to search for the Keplerian velocity
* \li \c icontrol(8) = mer_mag : step at which the electromagnetic
* part is switched on
* \li \c icontrol(9) = mer_change_mag : step at which the amplitude
* of the current/charge coupling function is changed
* to reach a_j0 or Q
* \li \c icontrol(10) = mer_fix_mag : step at which the final
* current/charge amplitude a_j0 or Q must have
* been reached
* \li \c icontrol(11) = conduc : flag 0 -> isolator material,
* 1 -> perfect conductor
*
* @param control [input] Set of parameters (stored as a
* 1-D \c Tbl of size 7) to control the
* iteration:
* \li \c control(0) = precis : threshold on the enthalpy relative
* change for ending the computation
* \li \c control(1) = omega_ini : initial angular velocity,
* switched on only if \c mer_rot < 0 ,
* otherwise 0 is used
* \li \c control(2) = relax : relaxation factor in the main
* iteration
* \li \c control(3) = relax_poisson : relaxation factor in
* \c Map_et::poisson
* \li \c control(4) = thres_adapt : threshold on dH/dr for
* freezing the adaptation of the mapping
* \li \c control(5) = ampli_triax : relative amplitude of
* the 3-D perturbation
* \li \c control(6) = precis_adapt : precision for
* \c Map_et::adapt
* \li \c control(7) = Q_ini : initial charge (total for the perfect
* conductor, per baryon for an isolator)
* \li \c control(8) = a_j_ini : initial amplitude for the coupling
* function
*
*
* @param mbar_wanted [input] Requested baryon mass (effective only
* if \c mer_mass>mer_max )
* @param aexp_mass [input] Exponent for the increase factor of the
* central enthalpy to converge to the
* requested baryon mass
* @param diff [output] 1-D \c Tbl of size 1 for the storage of
* some error indicators :
* \li \c diff(0) : Relative change in the enthalpy field
* between two successive steps
* @param Q0 [input] Requested electric charge for the case of a
* perfect conductor. Charge per baryon for the case
* of an isolator.
* @param a_j0 [input] Amplitude for the current/charge coupling function
*
* @param f_j [input] current or charge coupling function
* (see Bocquet et al. 1995).
*
* @param M_j [input] primitive (null for zero) of current/charge
* coupling function (see Bocquet et al. 1995)
* used for the first integral of stationary motion.
*/
void equilibrium_mag(double ent_c, double omega0, double fact_omega,
int nzadapt, const Tbl& ent_limit, const Itbl& icontrol,
const Tbl& control, double mbar_wanted, double aexp_mass,
Tbl& diff, const double Q0, const double a_j0,
Cmp (*f_j)(const Cmp& x, const double),
Cmp (*M_j)(const Cmp& x,const double));
/** Computes an equilibrium configuration.
*
* @param ent_c [input] Central enthalpy
* @param omega0 [input] Requested angular velocity
* (if \c fact_omega=1. )
* @param fact_omega [input] 1.01 = search for the Keplerian frequency,
* 1. = otherwise.
* @param nzadapt [input] Number of (inner) domains where the mapping
* adaptation to an iso-enthalpy surface
* should be performed
* @param ent_limit [input] 1-D \c Tbl of dimension \c nzet which
* defines the enthalpy at the outer boundary
* of each domain
* @param icontrol [input] Set of integer parameters (stored as a
* 1-D \c Itbl of size 8) to control the
* iteration:
* \li \c icontrol(0) = mer_max : maximum number of steps
* \li \c icontrol(1) = mer_rot : step at which the rotation is
* switched on
* \li \c icontrol(2) = mer_change_omega : step at which the rotation
* velocity is changed to reach the final one
* \li \c icontrol(3) = mer_fix_omega : step at which the final
* rotation velocity must have been reached
* \li \c icontrol(4) = mer_mass : the absolute value of
* \c mer_mass is the step from which the
* baryon mass is forced to converge,
* by varying the central enthalpy
* (\c mer_mass > 0 ) or the angular
* velocity (\c mer_mass < 0 )
* \li \c icontrol(5) = mermax_poisson : maximum number of steps in
* \c Map_et::poisson
* \li \c icontrol(6) = mer_triax : step at which the 3-D
* perturbation is switched on
* \li \c icontrol(7) = delta_mer_kep : number of steps
* after \c mer_fix_omega when \c omega
* starts to be increased by \c fact_omega
* to search for the Keplerian velocity
* \li \c icontrol(8) = mer_mag : step at which the electromagnetic
* part is switched on
* \li \c icontrol(9) = mer_change_mag : step at which the amplitude
* of the current/charge coupling function is changed
* to reach a_j0 or Q
* \li \c icontrol(10) = mer_fix_mag : step at which the final
* current/charge amplitude a_j0 or Q must have
* been reached
* \li \c icontrol(11) = conduc : flag 0 -> isolator material,
* 1 -> perfect conductor
*
* @param control [input] Set of parameters (stored as a
* 1-D \c Tbl of size 7) to control the
* iteration:
* \li \c control(0) = precis : threshold on the enthalpy relative
* change for ending the computation
* \li \c control(1) = omega_ini : initial angular velocity,
* switched on only if \c mer_rot < 0 ,
* otherwise 0 is used
* \li \c control(2) = relax : relaxation factor in the main
* iteration
* \li \c control(3) = relax_poisson : relaxation factor in
* \c Map_et::poisson
* \li \c control(4) = thres_adapt : threshold on dH/dr for
* freezing the adaptation of the mapping
* \li \c control(5) = ampli_triax : relative amplitude of
* the 3-D perturbation
* \li \c control(6) = precis_adapt : precision for
* \c Map_et::adapt
* \li \c control(7) = Q_ini : initial charge (total for the perfect
* conductor, per baryon for an isolator)
* \li \c control(8) = a_j_ini : initial amplitude for the coupling
* function
*
*
* @param mbar_wanted [input] Requested baryon mass (effective only
* if \c mer_mass>mer_max )
* @param aexp_mass [input] Exponent for the increase factor of the
* central enthalpy to converge to the
* requested baryon mass
* @param diff [output] 1-D \c Tbl of size 1 for the storage of
* some error indicators :
* \li \c diff(0) : Relative change in the enthalpy field
* between two successive steps
* @param Q0 [input] Requested electric charge for the case of a
* perfect conductor. Charge per baryon for the case
* of an isolator.
* @param a_j0 [input] Amplitude for the current/charge coupling function
*
* @param f_j [input] current or charge coupling function
* (see Bocquet et al. 1995).
*
* @param M_j [input] primitive (null for zero) of current/charge
* coupling function (see Bocquet et al. 1995)
* used for the first integral of stationary motion.
*/
void equilibrium_mag_plus( const Itbl& icontrol, const Tbl& control,
Tbl& diff,
const int initial_j,
const Tbl an_j,
Cmp (*f_j)(const Cmp& x, const Tbl),
Cmp (*M_j)(const Cmp& x,const Tbl),
const Tbl bn_j,
Cmp (*g_j)(const Cmp& x, const Tbl),
Cmp (*N_j)(const Cmp& x,const Tbl),
const double relax_mag);
};
class Et_magnetisation : public Et_rot_mag {
// Data :
// -----
protected:
///Flag : true if the value of the magnetic field is used in the Eos.
bool use_B_in_eos ;
///Flag : true if magnetisation terms are included in the equations.
bool include_magnetisation ;
Scalar xmag ; ///< The magnetisation scalar.
Scalar E_I; ///< Interaction (magnetisation) energy density.
///Interaction momentum density 3-vector.
Vector J_I;
///Interaction stress 3-tensor.
Sym_tensor Sij_I;
// Constructors - Destructor
// -------------------------
public:
/// Standard constructor
Et_magnetisation(Map& mp_i, int nzet_i, bool relat, const Eos& eos_i,
bool include_mag=true, bool use_B = true);
Et_magnetisation(const Et_magnetisation& ) ; ///< Copy constructor
/** Constructor from a file (see \c sauve(FILE*) ).
*
* @param mp_i Mapping on which the star will be defined
* @param eos_i Equation of state of the stellar matter
* @param fich input file (must have been created by the function
* \c sauve )
*/
Et_magnetisation(Map& mp_i, const Eos& eos_i, FILE* fich) ;
virtual ~Et_magnetisation() ; ///< Destructor
// Mutators / assignment
// ---------------------
public:
/// Assignment to another Et_rot_mag
void operator=(const Et_magnetisation&) ;
/** Computes the proper baryon and energy density, as well as
* pressure from the enthalpy.
*/
virtual void equation_of_state() ;
// Accessors
// ---------
public:
///Public accessor to the \c use_B_in_eos flag.
bool B_in_eos() const {return use_B_in_eos;};
///Public accessor to the \c include_magnetisation flag.
bool use_magnetisation() const {return include_magnetisation;} ;
///Accessor to the magnetisation scalar field.
const Scalar& get_magnetisation() const {return xmag;} ;
///Accessor to the interaction energy density.
const Scalar& get_E_I() const {return E_I;} ;
///Accessor to the interaction momentum vector.
const Vector& get_J_I() const {return J_I;} ;
///Accessor to the interaction stress tensor.
const Sym_tensor& get_Sij_I() const {return Sij_I;} ;
// Outputs
// -------
public:
virtual void sauve(FILE* ) const ; ///< Save in a file
/// Operator >> (virtual function called by the operator <<).
virtual ostream& operator>>(ostream& ) const ;
// Global quantities
// -----------------
public:
virtual double mass_g() const ; ///< Gravitational mass
virtual double angu_mom() const ; ///< Angular momentum
virtual double grv2() const ; ///< Error on the virial identity GRV2
/** Error on the virial identity GRV3.
* The error is computed as the integral defined
* by Eq. (43) of [Gourgoulhon and Bonazzola,
* \a Class. \a Quantum \a Grav. \b 11 , 443 (1994)] divided by
* the integral of the matter terms.
*
* @param ost output stream to give details of the computation;
* if set to 0x0 [default value], no details will be
* given.
*
*/
virtual double grv3(ostream* ost = 0x0) const ;
/** Part of the quadrupole moment.
* This term \f${\bar Q }\f$ is defined by Laarakkers and Poisson,
* \a Astrophys. \a J. \b 512 , 282 (1999). Note that \f${\bar Q }\f$
* is the negative of the (wrong) quadrupole moment defined in Eq. (7) of
* [Salgado, Bonazzola, Gourgoulhon and Haensel, \a Astron. \a Astrophys.
* \b 291 , 155 (1994)].
*/
virtual double mom_quad_old() const ;
/** Part of the quadrupole moment.
* \f$B_o\f$ is defined as \f$bM^2\f$, where \e b is given by Eq. (3.37) of
* [Friedman and Stergioulas, \a Rotating \a Relativistic \a Stars,
* Cambridge Monograph on mathematical physics] and \e M is the
* the gravitational mass of the star.
*/
virtual double mom_quad_Bo() const ;
// Computational routines
// ----------------------
public:
/** Computes the electromagnetic quantities solving the Maxwell
* equations (6) and (7) of [Bocquet, Bonazzola, Gourgoulhon and
* Novak, \a Astron. \a Astrophys. \b 301 , 757 (1995)]. In the case
* of a perfect conductor, le electromagnetic potential may have
* a discontinuous derivative across star's surface.
*
* @param conduc [input] flag: 0 for an isolator, 1 for a perfect
* conductor
* @param adapt_flag [input] flag: if 0 the mapping is NOT adapted
* to star's surface
* @param f_j [input] current or charge coupling function
* (see Bocquet et al. 1995).
* @param par_poisson_At [input] parameters for controlling the
* solution of the Poisson equation
* for At potential (see file
* et_rot_mag_equil.C)
* @param par_poisson_Avect [input] parameters for controlling the
* solution of vector Poisson equation
* for magnetic potential (see file
* et_rot_mag_equil.C)
*/
virtual void magnet_comput(const int adapt_flag,
Cmp (*f_j)(const Cmp& x, const double),
Param& par_poisson_At, Param& par_poisson_Avect) ;
/// Computes the electromagnetic part of the stress-energy tensor
virtual void MHD_comput() ;
/** Computes an equilibrium configuration.
*
* @param ent_c [input] Central enthalpy
* @param omega0 [input] Requested angular velocity
* (if \c fact_omega=1. )
* @param fact_omega [input] 1.01 = search for the Keplerian frequency,
* 1. = otherwise.
* @param nzadapt [input] Number of (inner) domains where the mapping
* adaptation to an iso-enthalpy surface
* should be performed
* @param ent_limit [input] 1-D \c Tbl of dimension \c nzet which
* defines the enthalpy at the outer boundary
* of each domain
* @param icontrol [input] Set of integer parameters (stored as a
* 1-D \c Itbl of size 11) to control the
* iteration:
* \li \c icontrol(0) = mer_max : maximum number of steps
* \li \c icontrol(1) = mer_rot : step at which the rotation is
* switched on
* \li \c icontrol(2) = mer_change_omega : step at which the rotation
* velocity is changed to reach the final one
* \li \c icontrol(3) = mer_fix_omega : step at which the final
* rotation velocity must have been reached
* \li \c icontrol(4) = mer_mass : the absolute value of
* \c mer_mass is the step from which the
* baryon mass is forced to converge,
* by varying the central enthalpy
* (\c mer_mass > 0 ) or the angular
* velocity (\c mer_mass < 0 )
* \li \c icontrol(5) = mermax_poisson : maximum number of steps in
* \c Map_et::poisson
* \li \c icontrol(6) = delta_mer_kep : number of steps
* after \c mer_fix_omega when \c omega
* starts to be increased by \c fact_omega
* to search for the Keplerian velocity
* \li \c icontrol(7) = mer_mag : step at which the electromagnetic
* part is switched on
* \li \c icontrol(8) = mer_change_mag : step at which the amplitude
* of the current/charge coupling function is changed
* to reach a_j0 or Q
* \li \c icontrol(9) = mer_fix_mag : step at which the final
* current/charge amplitude a_j0 or Q must have
* been reached
* \li \c icontrol(10) = mer_magmom : step from which the
* magnetic moment is forced to converge,
* by varying the current function amplitude.
*
* @param control [input] Set of parameters (stored as a
* 1-D \c Tbl of size 8) to control the
* iteration:
* \li \c control(0) = precis : threshold on the enthalpy relative
* change for ending the computation
* \li \c control(1) = omega_ini : initial angular velocity,
* switched on only if \c mer_rot < 0 ,
* otherwise 0 is used
* \li \c control(2) = relax : relaxation factor in the main
* iteration
* \li \c control(3) = relax_poisson : relaxation factor in
* \c Map_et::poisson
* \li \c control(4) = thres_adapt : threshold on dH/dr for
* freezing the adaptation of the mapping
* \li \c control(5) = precis_adapt : precision for
* \c Map_et::adapt
* \li \c control(6) = Q_ini : initial charge (total for the perfect
* conductor, per baryon for an isolator)
* \li \c control(7) = a_j_ini : initial amplitude for the coupling
* function
*
*
* @param mbar_wanted [input] Requested baryon mass (effective only
* if \c mer_mass>mer_max )
* @param aexp_mass [input] Exponent for the increase factor of the
* central enthalpy to converge to the
* requested baryon mass
* @param diff [output] 1-D \c Tbl of size 1 for the storage of
* some error indicators :
* \li \c diff(0) : Relative change in the enthalpy field
* between two successive steps
* @param Q0 [input] Requested electric charge for the case of a
* perfect conductor. Charge per baryon for the case
* of an isolator.
* @param a_j0 [input] Amplitude for the current/charge coupling function
*
* @param f_j [input] current or charge coupling function
* (see Bocquet et al. 1995).
*
* @param M_j [input] primitive (null for zero) of current/charge
* coupling function (see Bocquet et al. 1995)
* used for the first integral of stationary motion.
*/
void equilibrium_mag(double ent_c, double omega0, double fact_omega,
int nzadapt, const Tbl& ent_limit, const Itbl& icontrol,
const Tbl& control, double mbar_wanted,
double magmom_wanted, double aexp_mass,
Tbl& diff, double Q0, double a_j0,
Cmp (*f_j)(const Cmp& x, const double),
Cmp (*M_j)(const Cmp& x,const double));
};
}
#endif
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