1 | // |
---|
2 | // ******************************************************************** |
---|
3 | // * License and Disclaimer * |
---|
4 | // * * |
---|
5 | // * The Geant4 software is copyright of the Copyright Holders of * |
---|
6 | // * the Geant4 Collaboration. It is provided under the terms and * |
---|
7 | // * conditions of the Geant4 Software License, included in the file * |
---|
8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
---|
9 | // * include a list of copyright holders. * |
---|
10 | // * * |
---|
11 | // * Neither the authors of this software system, nor their employing * |
---|
12 | // * institutes,nor the agencies providing financial support for this * |
---|
13 | // * work make any representation or warranty, express or implied, * |
---|
14 | // * regarding this software system or assume any liability for its * |
---|
15 | // * use. Please see the license in the file LICENSE and URL above * |
---|
16 | // * for the full disclaimer and the limitation of liability. * |
---|
17 | // * * |
---|
18 | // * This code implementation is the result of the scientific and * |
---|
19 | // * technical work of the GEANT4 collaboration. * |
---|
20 | // * By using, copying, modifying or distributing the software (or * |
---|
21 | // * any work based on the software) you agree to acknowledge its * |
---|
22 | // * use in resulting scientific publications, and indicate your * |
---|
23 | // * acceptance of all terms of the Geant4 Software license. * |
---|
24 | // ******************************************************************** |
---|
25 | // |
---|
26 | // |
---|
27 | // $Id: G4MagHelicalStepper.cc,v 1.24 2010/07/14 10:00:36 gcosmo Exp $ |
---|
28 | // GEANT4 tag $Name: field-V09-03-03 $ |
---|
29 | // |
---|
30 | // -------------------------------------------------------------------- |
---|
31 | |
---|
32 | #include "G4MagHelicalStepper.hh" |
---|
33 | #include "G4LineSection.hh" |
---|
34 | #include "G4Mag_EqRhs.hh" |
---|
35 | |
---|
36 | // given a purely magnetic field a better approach than adding a straight line |
---|
37 | // (as in the normal runge-kutta-methods) is to add helix segments to the |
---|
38 | // current position |
---|
39 | |
---|
40 | |
---|
41 | // Constant for determining unit conversion when using normal as integrand. |
---|
42 | // |
---|
43 | const G4double G4MagHelicalStepper::fUnitConstant = 0.299792458*(GeV/(tesla*m)); |
---|
44 | |
---|
45 | |
---|
46 | G4MagHelicalStepper::G4MagHelicalStepper(G4Mag_EqRhs *EqRhs) |
---|
47 | : G4MagIntegratorStepper(EqRhs, 6), // integrate over 6 variables only !! |
---|
48 | // position & velocity |
---|
49 | fPtrMagEqOfMot(EqRhs), fAngCurve(0.), frCurve(0.), frHelix(0.) |
---|
50 | { |
---|
51 | } |
---|
52 | |
---|
53 | G4MagHelicalStepper::~G4MagHelicalStepper() |
---|
54 | { |
---|
55 | } |
---|
56 | |
---|
57 | void |
---|
58 | G4MagHelicalStepper::AdvanceHelix( const G4double yIn[], |
---|
59 | G4ThreeVector Bfld, |
---|
60 | G4double h, |
---|
61 | G4double yHelix[], |
---|
62 | G4double yHelix2[] ) |
---|
63 | { |
---|
64 | // const G4int nvar = 6; |
---|
65 | |
---|
66 | // OLD const G4double approc_limit = 0.05; |
---|
67 | // OLD approc_limit = 0.05 gives max.error=x^5/5!=(0.05)^5/5!=2.6*e-9 |
---|
68 | // NEW approc_limit = 0.005 gives max.error=x^5/5!=2.6*e-14 |
---|
69 | |
---|
70 | const G4double approc_limit = 0.005; |
---|
71 | G4ThreeVector Bnorm, B_x_P, vperp, vpar; |
---|
72 | |
---|
73 | G4double B_d_P; |
---|
74 | G4double B_v_P; |
---|
75 | G4double Theta; |
---|
76 | G4double R_1; |
---|
77 | G4double R_Helix; |
---|
78 | G4double CosT2, SinT2, CosT, SinT; |
---|
79 | G4ThreeVector positionMove, endTangent; |
---|
80 | |
---|
81 | G4double Bmag = Bfld.mag(); |
---|
82 | const G4double *pIn = yIn+3; |
---|
83 | G4ThreeVector initVelocity= G4ThreeVector( pIn[0], pIn[1], pIn[2]); |
---|
84 | G4double velocityVal = initVelocity.mag(); |
---|
85 | G4ThreeVector initTangent = (1.0/velocityVal) * initVelocity; |
---|
86 | |
---|
87 | R_1=GetInverseCurve(velocityVal,Bmag); |
---|
88 | |
---|
89 | // for too small magnetic fields there is no curvature |
---|
90 | // (include momentum here) FIXME |
---|
91 | |
---|
92 | if( (std::fabs(R_1) < 1e-10)||(Bmag<1e-12) ) |
---|
93 | { |
---|
94 | LinearStep( yIn, h, yHelix ); |
---|
95 | |
---|
96 | // Store and/or calculate parameters for chord distance |
---|
97 | |
---|
98 | SetAngCurve(1.); |
---|
99 | SetCurve(h); |
---|
100 | SetRadHelix(0.); |
---|
101 | } |
---|
102 | else |
---|
103 | { |
---|
104 | Bnorm = (1.0/Bmag)*Bfld; |
---|
105 | |
---|
106 | // calculate the direction of the force |
---|
107 | |
---|
108 | B_x_P = Bnorm.cross(initTangent); |
---|
109 | |
---|
110 | // parallel and perp vectors |
---|
111 | |
---|
112 | B_d_P = Bnorm.dot(initTangent); // this is the fraction of P parallel to B |
---|
113 | |
---|
114 | vpar = B_d_P * Bnorm; // the component parallel to B |
---|
115 | vperp= initTangent - vpar; // the component perpendicular to B |
---|
116 | |
---|
117 | B_v_P = std::sqrt( 1 - B_d_P * B_d_P); // Fraction of P perp to B |
---|
118 | |
---|
119 | // calculate the stepping angle |
---|
120 | |
---|
121 | Theta = R_1 * h; // * B_v_P; |
---|
122 | |
---|
123 | // Trigonometrix |
---|
124 | |
---|
125 | if( std::fabs(Theta) > approc_limit ) |
---|
126 | { |
---|
127 | SinT = std::sin(Theta); |
---|
128 | CosT = std::cos(Theta); |
---|
129 | } |
---|
130 | else |
---|
131 | { |
---|
132 | G4double Theta2 = Theta*Theta; |
---|
133 | G4double Theta3 = Theta2 * Theta; |
---|
134 | G4double Theta4 = Theta2 * Theta2; |
---|
135 | SinT = Theta - 1.0/6.0 * Theta3; |
---|
136 | CosT = 1 - 0.5 * Theta2 + 1.0/24.0 * Theta4; |
---|
137 | } |
---|
138 | |
---|
139 | // the actual "rotation" |
---|
140 | |
---|
141 | G4double R = 1.0 / R_1; |
---|
142 | |
---|
143 | positionMove = R * ( SinT * vperp + (1-CosT) * B_x_P) + h * vpar; |
---|
144 | endTangent = CosT * vperp + SinT * B_x_P + vpar; |
---|
145 | |
---|
146 | // Store the resulting position and tangent |
---|
147 | |
---|
148 | yHelix[0] = yIn[0] + positionMove.x(); |
---|
149 | yHelix[1] = yIn[1] + positionMove.y(); |
---|
150 | yHelix[2] = yIn[2] + positionMove.z(); |
---|
151 | yHelix[3] = velocityVal * endTangent.x(); |
---|
152 | yHelix[4] = velocityVal * endTangent.y(); |
---|
153 | yHelix[5] = velocityVal * endTangent.z(); |
---|
154 | |
---|
155 | // Store 2*h step Helix if exist |
---|
156 | |
---|
157 | if(yHelix2) |
---|
158 | { |
---|
159 | SinT2 = 2.0 * SinT * CosT; |
---|
160 | CosT2 = 1.0 - 2.0 * SinT * SinT; |
---|
161 | endTangent = (CosT2 * vperp + SinT2 * B_x_P + vpar); |
---|
162 | positionMove = R * ( SinT2 * vperp + (1-CosT2) * B_x_P) + h*2 * vpar; |
---|
163 | |
---|
164 | yHelix2[0] = yIn[0] + positionMove.x(); |
---|
165 | yHelix2[1] = yIn[1] + positionMove.y(); |
---|
166 | yHelix2[2] = yIn[2] + positionMove.z(); |
---|
167 | yHelix2[3] = velocityVal * endTangent.x(); |
---|
168 | yHelix2[4] = velocityVal * endTangent.y(); |
---|
169 | yHelix2[5] = velocityVal * endTangent.z(); |
---|
170 | } |
---|
171 | |
---|
172 | // Store and/or calculate parameters for chord distance |
---|
173 | |
---|
174 | G4double ptan=velocityVal*B_v_P; |
---|
175 | |
---|
176 | G4double particleCharge = fPtrMagEqOfMot->FCof() / (eplus*c_light); |
---|
177 | R_Helix =std::abs( ptan/(fUnitConstant * particleCharge*Bmag)); |
---|
178 | |
---|
179 | SetAngCurve(std::abs(Theta)); |
---|
180 | SetCurve(std::abs(R)); |
---|
181 | SetRadHelix(R_Helix); |
---|
182 | } |
---|
183 | } |
---|
184 | |
---|
185 | // |
---|
186 | // Use the midpoint method to get an error estimate and correction |
---|
187 | // modified from G4ClassicalRK4: W.Wander <wwc@mit.edu> 12/09/97 |
---|
188 | // |
---|
189 | |
---|
190 | void |
---|
191 | G4MagHelicalStepper::Stepper( const G4double yInput[], |
---|
192 | const G4double*, |
---|
193 | G4double hstep, |
---|
194 | G4double yOut[], |
---|
195 | G4double yErr[] ) |
---|
196 | { |
---|
197 | const G4int nvar = 6; |
---|
198 | |
---|
199 | G4int i; |
---|
200 | |
---|
201 | // correction for Richardson Extrapolation. |
---|
202 | // G4double correction = 1. / ( (1 << IntegratorOrder()) -1 ); |
---|
203 | |
---|
204 | G4double yTemp[7], yIn[7] ; |
---|
205 | G4ThreeVector Bfld_initial, Bfld_midpoint; |
---|
206 | |
---|
207 | // Saving yInput because yInput and yOut can be aliases for same array |
---|
208 | |
---|
209 | for(i=0;i<nvar;i++) { yIn[i]=yInput[i]; } |
---|
210 | |
---|
211 | G4double h = hstep * 0.5; |
---|
212 | |
---|
213 | MagFieldEvaluate(yIn, Bfld_initial) ; |
---|
214 | |
---|
215 | // Do two half steps |
---|
216 | |
---|
217 | DumbStepper(yIn, Bfld_initial, h, yTemp); |
---|
218 | MagFieldEvaluate(yTemp, Bfld_midpoint) ; |
---|
219 | DumbStepper(yTemp, Bfld_midpoint, h, yOut); |
---|
220 | |
---|
221 | // Do a full Step |
---|
222 | |
---|
223 | h = hstep ; |
---|
224 | DumbStepper(yIn, Bfld_initial, h, yTemp); |
---|
225 | |
---|
226 | // Error estimation |
---|
227 | |
---|
228 | for(i=0;i<nvar;i++) |
---|
229 | { |
---|
230 | yErr[i] = yOut[i] - yTemp[i] ; |
---|
231 | } |
---|
232 | |
---|
233 | return; |
---|
234 | } |
---|
235 | |
---|
236 | G4double |
---|
237 | G4MagHelicalStepper::DistChord() const |
---|
238 | { |
---|
239 | // Check whether h/R > pi !! |
---|
240 | // Method DistLine is good only for < pi |
---|
241 | |
---|
242 | G4double Ang=GetAngCurve(); |
---|
243 | if(Ang<=pi) |
---|
244 | { |
---|
245 | return GetRadHelix()*(1-std::cos(0.5*Ang)); |
---|
246 | } |
---|
247 | else |
---|
248 | { |
---|
249 | if(Ang<twopi) |
---|
250 | { |
---|
251 | return GetRadHelix()*(1+std::cos(0.5*(twopi-Ang))); |
---|
252 | } |
---|
253 | else // return Diameter of projected circle |
---|
254 | { |
---|
255 | return 2*GetRadHelix(); |
---|
256 | } |
---|
257 | } |
---|
258 | } |
---|