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// MAUS WARNING: THIS IS LEGACY CODE.
/* This file is part of MAUS: http://micewww.pp.rl.ac.uk/projects/maus
*
* MAUS 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 3 of the License, or
* (at your option) any later version.
*
* MAUS 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 MAUS. If not, see <http://www.gnu.org/licenses/>.
*
*/
#include "CLHEP/Units/PhysicalConstants.h"
#include "gsl/gsl_sf_gamma.h"
#include "gsl/gsl_sf_pow_int.h"
#include "gsl/gsl_odeiv.h"
#include "gsl/gsl_errno.h"
#include "BeamTools/BTMultipole.hh"
#include "Utils/Exception.hh"
#include "Interface/Squeak.hh"
const BTMultipole * BTMultipole::staticMultipole = NULL;
double BTMultipole::staticDX = 0.;
double BTMultipole::_relativeError = 1.e-5;
double BTMultipole::_absoluteError = 1.e-5;
double BTMultipole::_stepSize = 1.;
BTMultipole::BTMultipole()
: _pole(0), _magnitude(0.), _length(0.), _rCurv(0.),
_height(0.), _width(0.), _curvature(constant),
_endFieldModel(NULL) {
}
void BTMultipole::Init(int pole, double fieldAtWidth,
double length, double height, double width,
std::string curvature, double radiusVariable,
const EndFieldModel* endfield, int endPole) {
_pole = pole;
_magnitude = fieldAtWidth;
_length = length;
_rCurv = radiusVariable;
_height = height;
_width = width;
_curvature = constant;
_endFieldPole = endPole;
_endFieldModel = NULL;
if (endfield != NULL) _endFieldModel = endfield->Clone();
if (curvature == "MomentumBased") {
_curvature = momentumBased;
_momentum = radiusVariable;
_rCurv = 0;
_magnitude = 1.;
SetupDipoleMagnitude(radiusVariable, fieldAtWidth);
SetupReferenceTrajectory();
} else {
if (fabs(radiusVariable) < 1e-5 || curvature == "Straight") {
_curvature = straight;
} else {
if (curvature == "StraightEnds") _curvature = straightEnds;
if (curvature == "Constant" || curvature == "") _curvature = constant;
if (_width >= fabs(_rCurv))
throw(MAUS::Exception(MAUS::Exception::nonRecoverable,
"Multipole with width > radius of curvature",
"BTMultipole::BTMultipole"));
if (_length > fabs(2*pi*_rCurv))
throw(MAUS::Exception(MAUS::Exception::nonRecoverable,
"Multipole with bending angle > 360 degrees",
"BTMultipole::BTMultipole"));
_endRotation = CLHEP::HepRotation(CLHEP::Hep3Vector(0, 1, 0),
_length/_rCurv);
_endPoint = _endRotation*CLHEP::Hep3Vector(-_rCurv, 0, 0)+
CLHEP::Hep3Vector(_rCurv, 0, 0);
}
}
bbMin[0] = -_width;
bbMax[0] = +_width;
bbMin[1] = -_height;
bbMax[1] = +_height;
bbMin[2] = 0.;
bbMax[2] = _length*2.;
}
BTMultipole BTMultipole::DipoleFromMomentum
(double momentum, double length, double angle, double height, double width) {
// field = theta p / (qL)
// rcurv = l / theta
double field = (2*pi*angle/360.)*momentum/length/CLHEP::eplus/c_light;
double rCurv = length*360./(2*pi*angle); // L = 2 pi r*(theta/360)
BTMultipole m;
m.Init(1, field, length, height, width, "constant", rCurv, NULL, 0);
return m;
}
CLHEP::Hep3Vector BTMultipole::TransformToRotated(const double * Point) const {
switch (_curvature) {
case straight:
return CLHEP::Hep3Vector(Point[0], Point[1], Point[2]);
case constant:
return TransformToRotatedConstant(Point);
case straightEnds:
return TransformToRotatedStraightEnds(Point);
case momentumBased:
return TransformToRotatedMomentumBased(Point);
default:
throw(MAUS::Exception(MAUS::Exception::nonRecoverable, "Did not recognise curvature model",
"BTMultipole::TransformToRotated(const double*)"));
}
}
CLHEP::Hep3Vector BTMultipole::TransformToRotatedMomentumBased
(const double point[3]) const {
int p0 = 0;
int p1 = _refX.size()-1;
double rSquaredStart = (point[0]-_refX[p0])*(point[0]-_refX[p0]) +
(point[2]-_refZ[p0])*(point[2]-_refZ[p0]);
double rSquaredEnd = (point[0]-_refX[p1])*(point[0]-_refX[p1]) +
(point[2]-_refZ[p1])*(point[2]-_refZ[p1]);
// This is horrid!!! Minimise rSquared (using binary interpolation) to find
// s(x,z) Assumes sign(B) == const st dRSquared is always increasing or
// decreasing
while (unsigned(p1-p0)>1) {
int pM = (p1+p0)/2;
double rSquaredMiddle = (point[0]-_refX[pM])*(point[0]-_refX[pM]) +
(point[2]-_refZ[pM])*(point[2]-_refZ[pM]);
if (rSquaredStart > rSquaredEnd) {
rSquaredStart = rSquaredMiddle;
p0 = pM;
} else {
rSquaredEnd = rSquaredMiddle;
p1 = pM;
}
}
double deltaR = sqrt(rSquaredStart);
if (point[0]-_refX[p0] > 0.) deltaR *= -1;
double deltaS = _refS[p0];
return CLHEP::Hep3Vector(deltaR, point[1], deltaS);
}
CLHEP::Hep3Vector BTMultipole::TransformToRotatedConstant
(const double * Point) const {
double x = Point[0];
double z = Point[2];
if (x == -_rCurv) return CLHEP::Hep3Vector(_rCurv, Point[1], 0.);
double q = atan2(z, x+_rCurv);
double deltaS = q*_rCurv/2*pi;
double deltaR = sqrt(gsl_sf_pow_int(x+_rCurv, 2)+z*z)-_rCurv;
return CLHEP::Hep3Vector(deltaR, Point[1], deltaS);
}
CLHEP::Hep3Vector BTMultipole::TransformToRotatedStraightEnds
(const double * Point) const {
if (Point[2] < 0.5*(_length-_centreLength))
return CLHEP::Hep3Vector(Point[0], Point[1], Point[2]);
double pos[3] = {Point[0], Point[1], Point[2]-0.5*(_length-_centreLength)};
CLHEP::Hep3Vector trans = TransformToRotatedConstant(pos);
if (trans[2] > _centreLength)
trans = _endRotation*(trans-_endPoint)+_endPoint;
trans[2] += 0.5*(_length-_centreLength);
return trans;
}
double BTMultipole::RadiusOfCurvature(double sRelativeToEnd) const {
switch (_curvature) {
case straight:
return 0;
case constant:
return _rCurv;
case straightEnds:
if (sRelativeToEnd > 0.) {
return 0;
} else {
return _rCurv;
}
case momentumBased: {
double EMfield[3] = {0, 0, 0};
GetFieldValueRotated(CLHEP::Hep3Vector(0, 0, sRelativeToEnd), EMfield);
return _momentum/EMfield[1]/CLHEP::eplus/CLHEP::c_light;
}
default:
throw(MAUS::Exception(MAUS::Exception::nonRecoverable, "Did not recognise curvature model",
"BTMultipole::RadiusOfCurvature(double)"));
}
}
void BTMultipole::TransformToRectangular
(const double point[3], double* value) const {
switch (_curvature) {
case straight:
return;
case constant:
return TransformToRectangularConstant(point, value);
case straightEnds:
return TransformToRectangularStraightEnds(point, value);
case momentumBased:
return TransformToRectangularMomentumBased(point, value);
default:
throw(MAUS::Exception(MAUS::Exception::nonRecoverable, "Did not recognise curvature model",
"BTMultipole::TransformToRectangular(const double*, double*)"));
}
}
void BTMultipole::TransformToRectangularConstant
(const double point[3], double* value) const {
double theta = atan2(point[2], point[0]+_rCurv);
double bx = value[2]*sin(theta) + value[0]*cos(theta);
double bz = value[2]*cos(theta) + value[0]*sin(theta);
value[0] = bx;
value[2] = bz;
}
void BTMultipole::TransformToRectangularStraightEnds
(const double point[3], double* value) const {
if (point[2] < 0) return;
double theta = 0;
if (point[2] > _endPoint[2])
theta = _endRotation.delta();
else
theta = atan2(point[2], point[0]+_rCurv);
double bx = value[2]*sin(theta) + value[0]*cos(theta);
double bz = value[2]*cos(theta) + value[0]*sin(theta);
value[0] = bx;
value[2] = bz;
}
void BTMultipole::TransformToRectangularMomentumBased
(const double point[3], double* value) const {
int step = static_cast<int>(point[2]/_stepSize)+1;
double theta = 0;
if (step > static_cast<int>(_angle.size())) theta = _angle.back();
else if (step > 0) theta = _angle[step];
double bx = value[2]*sin(theta) + value[0]*cos(theta);
double bz = value[2]*cos(theta) + value[0]*sin(theta);
value[0] = bx;
value[2] = bz;
}
void BTMultipole::GetFieldValueRotated
(CLHEP::Hep3Vector pos, double *EMfield) const {
if (_endFieldModel == NULL) {
HardEdgedFieldValue(pos, EMfield);
return;
}
EndFieldValue(pos, EMfield);
}
void BTMultipole::GetFieldValue
(const double Point[4], double *EMfield) const {
CLHEP::Hep3Vector pos = TransformToRotated(Point);
GetFieldValueRotated(pos, EMfield);
TransformToRectangular(Point, EMfield);
return;
}
// pos is the position from the radius of curvature arc relative to the centre
// of the multipole - units?
void BTMultipole::HardEdgedFieldValue
(CLHEP::Hep3Vector pos, double *field) const {
if (pos.z() < 0. || pos.z() > _length) return;
if (fabs(pos.x()) > _width/2.) return;
if (fabs(pos.y()) > _height/2.) return;
for (int m = 1; m <= _pole; m+=2) {
double alpha = GetConst(0, _pole, m);
if (_pole-m-1 >= 0.)
field[0] += alpha*((_pole-m)*gsl_sf_pow_int(pos.x(), _pole-m-1)*
gsl_sf_pow_int(pos.y(), m));
if (m-1 >= 0. && _pole-m >= 0.)
field[1] += alpha*((m)*gsl_sf_pow_int(pos.x(), _pole-m)*
gsl_sf_pow_int(pos.y(), m-1));
// hard edge => bz=0
}
for (int i = 0; i < 3; ++i) field[i] *= _magnitude;
}
double BTMultipole::GetConst(int q, int n, int m) {
return gsl_sf_pow_int(gsl_sf_fact(n), 2)*gsl_sf_pow_int(-1, (m-1)/2)/(
gsl_sf_pow_int(-4, q)*gsl_sf_fact(q)*gsl_sf_fact(n+q)*gsl_sf_fact(m)
*gsl_sf_fact(n-m))/static_cast<double>(n);
}
void BTMultipole::EndFieldValue(CLHEP::Hep3Vector pos, double *field) const {
if (pos.z() < 0. || pos.z() > _length) return;
if (fabs(pos.x()) > _width/2.) return;
if (fabs(pos.y()) > _height/2.) return;
pos[2] -= _length/2.;
int n(_pole);
const double x = pos[0];
const double y = pos[1];
const double z = pos[2];
for (int q = 0; q <= _endFieldPole; ++q) {
double f = _endFieldModel->Function(z, 2*q);
double fPrime = _endFieldModel->Function(z, 2*q+1);
for (int m = 1; m <= n; m += 2) {
double const_qnm = GetConst(q, n, m);
if ( q > 0 )
field[0] += const_qnm*f*(2.*q*x*gsl_sf_pow_int((x*x+y*y), q-1)
*gsl_sf_pow_int(x, n-m)*gsl_sf_pow_int(y, m));
if (n-m > 0)
field[0] += const_qnm*f*(n-m)*gsl_sf_pow_int((x*x+y*y), q)
*gsl_sf_pow_int(x, n-m-1)*gsl_sf_pow_int(y, m);
if (m > 0)
field[1] += const_qnm*f*m*gsl_sf_pow_int(x*x+y*y, q)
*gsl_sf_pow_int(x, n-m)*gsl_sf_pow_int(y, m-1);
if (q > 0)
field[1] += const_qnm*f*2*q*y*gsl_sf_pow_int(x*x+y*y, q-1)
*gsl_sf_pow_int(x, n-m)*gsl_sf_pow_int(y, m);
field[2] += const_qnm*fPrime*gsl_sf_pow_int(x*x+y*y, q)
*gsl_sf_pow_int(x, n-m)*gsl_sf_pow_int(y, m);
}
}
for (int i = 0; i < 3; ++i) field[i] *= _magnitude;
}
void BTMultipole::Print(std::ostream &out) const {
out << "Multipole Order: " << 2*_pole << " Length: " << _length
<< " Magnitude: " << _magnitude << " BendingRadius: " << _rCurv
<< " Height: " << _height << " Width: " << _width << " EndField: ";
if (_endFieldModel == NULL)
out << "HardEdged";
else
_endFieldModel->Print(out);
BTField::Print(out);
}
void BTMultipole::SetupReferenceTrajectory() {
_angle = _refX = _refS = _refZ = std::vector<double>();
staticMultipole = this;
const gsl_odeiv_step_type* T = gsl_odeiv_step_rk4;
gsl_odeiv_step* stepper = gsl_odeiv_step_alloc(T, 4);
gsl_odeiv_control* control = gsl_odeiv_control_y_new(_absoluteError,
_relativeError);
gsl_odeiv_evolve* evolve = gsl_odeiv_evolve_alloc(4);
gsl_odeiv_system system = {EvolveReferenceTrajectory, NULL, 4, NULL};
double h = 0.1;
double s = 0.;
double y[4] = {0, 0, 0, _momentum};
for (double sMax = s; sMax <= _length; sMax += _stepSize) {
while (s < sMax) {
int status = gsl_odeiv_evolve_apply(evolve, control, stepper, &system,
&s, sMax, &h, y);
if (status != GSL_SUCCESS) {
Print(Squeak::mout(Squeak::debug));
throw(MAUS::Exception(MAUS::Exception::nonRecoverable,
"Error calculating reference trajectory",
"BTMultipole::SetupReferenceTrajectory()"));
}
_refS.push_back(s);
_refX.push_back(y[0]);
_refZ.push_back(y[1]);
_angle.push_back(atan(y[2]/y[3]));
}
}
gsl_odeiv_evolve_free(evolve);
gsl_odeiv_control_free(control);
gsl_odeiv_step_free(stepper);
staticMultipole = NULL;
}
double BTMultipole::IntegralB(double dxOffset) const {
staticMultipole = this;
staticDX = dxOffset;
const gsl_odeiv_step_type * T = gsl_odeiv_step_rk4;
gsl_odeiv_step * stepper = gsl_odeiv_step_alloc(T, 1);
gsl_odeiv_control * control = gsl_odeiv_control_y_new(_absoluteError,
_relativeError);
gsl_odeiv_evolve * evolve = gsl_odeiv_evolve_alloc(1);
gsl_odeiv_system system = {EvolveIntegralB, NULL, 1, NULL};
double h = 10.;
double s = 0.;
double y[1] = {0};
int step = 0;
while (s < _length) {
if (step > 10000) {
Squeak::mout(Squeak::warning) << "Stepper stuck while calculating "
<< "BTMultipole Effective Length"
<< std::endl;
return 0.;
}
int status = gsl_odeiv_evolve_apply(evolve, control, stepper, &system, &s,
_length, &h, y);
if (status != GSL_SUCCESS) {
Print(Squeak::mout(Squeak::debug));
throw(MAUS::Exception(MAUS::Exception::nonRecoverable, "Error integrating reference By",
"BTMultipole::SetupMagnitude()"));
}
step++;
h = 10.;
}
gsl_odeiv_evolve_free(evolve);
gsl_odeiv_control_free(control);
gsl_odeiv_step_free(stepper);
staticMultipole = NULL;
return y[0];
}
void BTMultipole::SetupDipoleMagnitude(double momentum, double angleInRadians) {
double intB = IntegralB(0.); // integral B dl [T mm]
double theta = CLHEP::eplus*c_light/momentum*intB;
_magnitude = angleInRadians/theta;
}
int BTMultipole::EvolveReferenceTrajectory
(double s, const double y[], double f[], void *params) {
double bfield[3] = {0, 0, 0};
staticMultipole->GetFieldValueRotated(CLHEP::Hep3Vector(0, 0, s), bfield);
f[0] = y[2]/staticMultipole->_momentum; // dx/ds = px/ps
f[1] = y[3]/staticMultipole->_momentum; // dz/ds = pz/ps
f[2] = -CLHEP::eplus*c_light*f[1]*bfield[1]; // dpx/ds = -q*c*dz/ds*by
f[3] = CLHEP::eplus*c_light*f[0]*bfield[1]; // dpz/ds = q*c*dx/ds*by
return GSL_SUCCESS;
}
int BTMultipole::EvolveIntegralB
(double s, const double y[], double f[], void *params) {
double bfield[3] = {0, 0, 0};
staticMultipole->GetFieldValueRotated(Hep3Vector(staticDX, 0, s), bfield);
f[0] = bfield[1];
return GSL_SUCCESS;
}
void BTMultipole::GetReferenceTrajectory(std::vector<double>& x,
std::vector<double>& z, std::vector<double>& angle,
std::vector<double>& s) {
x = _refX;
z = _refZ;
angle = _angle;
s = _refS;
}
void BTMultipole::SetReferenceTrajectory(std::vector<double> x,
std::vector<double> z, std::vector<double> angle,
std::vector<double> s) {
_refX = x;
_refZ = z;
_refS = s;
_angle = angle;
}
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