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25 // 25 //
26 // G4EqEMFieldWithEDM implementation << 26 //
>> 27 // $Id: G4EqEMFieldWithEDM.cc,v 1.2 2009/11/06 22:31:54 gum Exp $
>> 28 // GEANT4 tag $Name: geant4-09-03-patch-01 $
>> 29 //
27 // 30 //
28 // This is the standard right-hand side for e 31 // This is the standard right-hand side for equation of motion.
29 // 32 //
30 // Created: Kevin Lynch, 19.02.2009 - Based on << 33 // 19.02.2009 Kevin Lynch, based on G4EqEMFieldWithSpin
31 // Modified: Hiromi Iinuma, 06.11.2009 - see: << 34 // 06.11.2009 Hiromi Iinuma see:
32 // http://hypernews.slac.stanford.edu/HyperN << 35 // http://hypernews.slac.stanford.edu/HyperNews/geant4/get/emfields/161.html
>> 36 //
33 // ------------------------------------------- 37 // -------------------------------------------------------------------
34 38
35 #include "G4EqEMFieldWithEDM.hh" 39 #include "G4EqEMFieldWithEDM.hh"
36 #include "G4ElectroMagneticField.hh" 40 #include "G4ElectroMagneticField.hh"
37 #include "G4ThreeVector.hh" 41 #include "G4ThreeVector.hh"
38 #include "globals.hh" 42 #include "globals.hh"
39 #include "G4PhysicalConstants.hh" <<
40 #include "G4SystemOfUnits.hh" <<
41 43
42 G4EqEMFieldWithEDM::G4EqEMFieldWithEDM(G4Elect << 44 G4EqEMFieldWithEDM::G4EqEMFieldWithEDM(G4ElectroMagneticField *emField )
43 : G4EquationOfMotion( emField ) << 45 : G4EquationOfMotion( emField )
44 { 46 {
>> 47 anomaly = 0.0011659208;
>> 48 eta = 0.;
45 } 49 }
46 50
47 G4EqEMFieldWithEDM::~G4EqEMFieldWithEDM() = de << 51 G4EqEMFieldWithEDM::~G4EqEMFieldWithEDM()
>> 52 {
>> 53 }
48 54
49 void 55 void
50 G4EqEMFieldWithEDM::SetChargeMomentumMass(G4Ch << 56 G4EqEMFieldWithEDM::SetChargeMomentumMass(G4double particleCharge, // e+ units
51 G4do << 57 G4double MomentumXc,
52 G4do << 58 G4double particleMass)
53 { 59 {
54 charge = particleCharge.GetCharge(); << 60 fElectroMagCof = eplus*particleCharge*c_light ;
55 mass = particleMass; << 61 fMassCof = particleMass*particleMass ;
56 magMoment = particleCharge.GetMagneticDipol << 62
57 spin = particleCharge.GetSpin(); << 63 omegac = 0.105658387*GeV/particleMass * 2.837374841e-3*(rad/cm/kilogauss);
58 <<
59 fElectroMagCof = eplus*charge*c_light; <<
60 fMassCof = mass*mass; <<
61 <<
62 omegac = (eplus/mass)*c_light; <<
63 <<
64 G4double muB = 0.5*eplus*hbar_Planck/(mass/ <<
65 <<
66 G4double g_BMT; <<
67 if ( spin != 0. ) <<
68 { <<
69 g_BMT = (std::abs(magMoment)/muB)/spin; <<
70 } <<
71 else <<
72 { <<
73 g_BMT = 2.; <<
74 } <<
75 64
76 anomaly = (g_BMT - 2.)/2.; << 65 ParticleCharge = particleCharge;
77 66
78 G4double E = std::sqrt(sqr(MomentumXc)+sqr( << 67 E = std::sqrt(sqr(MomentumXc)+sqr(particleMass));
79 beta = MomentumXc/E; 68 beta = MomentumXc/E;
80 gamma = E/mass; << 69 gamma = E/particleMass;
>> 70
81 } 71 }
82 72
83 void 73 void
84 G4EqEMFieldWithEDM::EvaluateRhsGivenB(const G4 74 G4EqEMFieldWithEDM::EvaluateRhsGivenB(const G4double y[],
85 const G4 << 75 const G4double Field[],
86 G4 << 76 G4double dydx[] ) const
87 { 77 {
88 78
89 // Components of y: 79 // Components of y:
90 // 0-2 dr/ds, 80 // 0-2 dr/ds,
91 // 3-5 dp/ds - momentum derivatives 81 // 3-5 dp/ds - momentum derivatives
92 // 9-11 dSpin/ds = (1/beta) dSpin/dt - s 82 // 9-11 dSpin/ds = (1/beta) dSpin/dt - spin derivatives
93 83
94 // The BMT equation, following J.D.Jackson, 84 // The BMT equation, following J.D.Jackson, Classical
95 // Electrodynamics, Second Edition, with ad 85 // Electrodynamics, Second Edition, with additions for EDM
96 // evolution from 86 // evolution from
97 // M.Nowakowski, et.al. Eur.J.Phys.26, pp 5 87 // M.Nowakowski, et.al. Eur.J.Phys.26, pp 545-560, (2005)
98 // or 88 // or
99 // Silenko, Phys.Rev.ST Accel.Beams 9:03400 89 // Silenko, Phys.Rev.ST Accel.Beams 9:034003, (2006)
100 90
101 // dS/dt = (e/m) S \cross 91 // dS/dt = (e/m) S \cross
102 // MDM: [ (g/2-1 +1/\gamma) B 92 // MDM: [ (g/2-1 +1/\gamma) B
103 // -(g/2-1)\gamma/(\gamma+1) 93 // -(g/2-1)\gamma/(\gamma+1) (\beta \cdot B)\beta
104 // -(g/2-\gamma/(\gamma+1) \b 94 // -(g/2-\gamma/(\gamma+1) \beta \cross E
105 // 95 //
106 // EDM: eta/2( E - gamma/(gamma+1) \ 96 // EDM: eta/2( E - gamma/(gamma+1) \beta (\beta \cdot E)
107 // + \beta \cross B ) ] 97 // + \beta \cross B ) ]
108 // 98 //
109 // where 99 // where
110 // S = \vec{s}, where S^2 = 1 100 // S = \vec{s}, where S^2 = 1
111 // B = \vec{B} 101 // B = \vec{B}
112 // \beta = \vec{\beta} = \beta \vec{u} with 102 // \beta = \vec{\beta} = \beta \vec{u} with u^2 = 1
113 // E = \vec{E} 103 // E = \vec{E}
114 104
115 G4double pSquared = y[3]*y[3] + y[4]*y[4] + 105 G4double pSquared = y[3]*y[3] + y[4]*y[4] + y[5]*y[5] ;
116 106
117 G4double Energy = std::sqrt( pSquared + f 107 G4double Energy = std::sqrt( pSquared + fMassCof );
118 G4double cof2 = Energy/c_light ; 108 G4double cof2 = Energy/c_light ;
119 109
120 G4double pModuleInverse = 1.0/std::sqrt(pS 110 G4double pModuleInverse = 1.0/std::sqrt(pSquared) ;
121 111
122 G4double inverse_velocity = Energy * pModul 112 G4double inverse_velocity = Energy * pModuleInverse / c_light;
123 113
124 G4double cof1 = fElectroMagCof*pModuleI 114 G4double cof1 = fElectroMagCof*pModuleInverse ;
125 115
126 dydx[0] = y[3]*pModuleInverse ; 116 dydx[0] = y[3]*pModuleInverse ;
127 dydx[1] = y[4]*pModuleInverse ; 117 dydx[1] = y[4]*pModuleInverse ;
128 dydx[2] = y[5]*pModuleInverse ; 118 dydx[2] = y[5]*pModuleInverse ;
129 119
130 dydx[3] = cof1*(cof2*Field[3] + (y[4]*Field 120 dydx[3] = cof1*(cof2*Field[3] + (y[4]*Field[2] - y[5]*Field[1])) ;
131 121
132 dydx[4] = cof1*(cof2*Field[4] + (y[5]*Field 122 dydx[4] = cof1*(cof2*Field[4] + (y[5]*Field[0] - y[3]*Field[2])) ;
133 123
134 dydx[5] = cof1*(cof2*Field[5] + (y[3]*Field 124 dydx[5] = cof1*(cof2*Field[5] + (y[3]*Field[1] - y[4]*Field[0])) ;
135 125
136 dydx[6] = dydx[8] = 0.;//not used 126 dydx[6] = dydx[8] = 0.;//not used
137 127
138 // Lab Time of flight 128 // Lab Time of flight
139 dydx[7] = inverse_velocity; 129 dydx[7] = inverse_velocity;
140 130
141 G4ThreeVector BField(Field[0],Field[1],Fiel 131 G4ThreeVector BField(Field[0],Field[1],Field[2]);
142 G4ThreeVector EField(Field[3],Field[4],Fiel 132 G4ThreeVector EField(Field[3],Field[4],Field[5]);
143 133
144 EField /= c_light; 134 EField /= c_light;
145 135
146 G4ThreeVector u(y[3], y[4], y[5]); 136 G4ThreeVector u(y[3], y[4], y[5]);
147 u *= pModuleInverse; 137 u *= pModuleInverse;
148 138
149 G4double udb = anomaly*beta*gamma/(1.+gamma 139 G4double udb = anomaly*beta*gamma/(1.+gamma) * (BField * u);
150 G4double ucb = (anomaly+1./gamma)/beta; 140 G4double ucb = (anomaly+1./gamma)/beta;
151 G4double uce = anomaly + 1./(gamma+1.); 141 G4double uce = anomaly + 1./(gamma+1.);
152 G4double ude = beta*gamma/(1.+gamma)*(EFiel 142 G4double ude = beta*gamma/(1.+gamma)*(EField*u);
153 143
154 G4ThreeVector Spin(y[9],y[10],y[11]); 144 G4ThreeVector Spin(y[9],y[10],y[11]);
155 145
156 G4double pcharge; << 146 G4ThreeVector dSpin
157 if (charge == 0.) << 147 = ParticleCharge*omegac*( ucb*(Spin.cross(BField))-udb*(Spin.cross(u))
158 { << 148 // from Jackson
159 pcharge = 1.; << 149 // -uce*Spin.cross(u.cross(EField)) )
160 } << 150 // but this form has one less operation
161 else << 151 - uce*(u*(Spin*EField) - EField*(Spin*u))
162 { << 152 +eta/2.*(Spin.cross(EField) - ude*(Spin.cross(u))
163 pcharge = charge; << 153 // +Spin.cross(u.cross(Bfield))
164 } << 154 + (u*(Spin*BField) - BField*(Spin*u))
165 << 155 )
166 G4ThreeVector dSpin(0.,0.,0.); << 156 );
167 if (Spin.mag2() != 0.) << 157
168 { <<
169 dSpin = pcharge*omegac*( ucb*(Spin.cross <<
170 // from Jacks <<
171 // -uce*Spin. <<
172 // but this f <<
173 - uce*(u*(Spin*EField <<
174 + eta/2.*(Spin.cross( <<
175 // +Spin.cros <<
176 + (u*(Spin*BField) - <<
177 } <<
178 <<
179 dydx[ 9] = dSpin.x(); 158 dydx[ 9] = dSpin.x();
180 dydx[10] = dSpin.y(); 159 dydx[10] = dSpin.y();
181 dydx[11] = dSpin.z(); 160 dydx[11] = dSpin.z();
182 161
183 return; << 162 return ;
184 } 163 }
185 164