g4beamline_ blengefunction class reference.pdf

8/10/2019 g4beamline_ BLEngeFunction Class Reference.pdf

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Ngy 8 thng 12 nm 2014 g4beamline: BLEngeFunction Class Reference

http://www.muonsinternal.com/muons3/g4beamline/Doxygen/classBLEngeFunction.html

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BLEngeFunction Class Reference

#include

List of all members.

Detailed Description

class EngeFunction implements the Enge function for fringe fields.

z is the distance from the nominal edge, with z=0 being the edge. it should be divided by the aperture diameter orfull width/height. z0 is outside.

See the COSY reference manual (pp 32-35) for suggested values of a1-a6, or use the ENGE_BEND orENGE_QUAD types (which come from there). http://cosy.pa.msu.edu/cosymanu/index.html

Mathematica was used to compute the derivatives.

Public Member Functions

BLEngeFunction ()

default constructor.

BLEngeFunction (BLEngeType t)

constructor for common magnet types.

BLEngeFunction (double _a1, double _a2, double _a3, double _a4, double _a5, double _a6)

general constructor.

void set(double _a1, double _a2, double _a3, double _a4, double _a5, double _a6)

set the parameters.

double operator()(double z) const

evaluate the Enge function at z.

double prime(double z) const

evaluate the derivative of the Enge funct ion at z.

double first(double z)

double second(double z) const

evaluate the second derivative of the Enge funct ion at z.

double third(double z) const

evaluate the third derivative of theEnge function at z.

double fourth(double z) const

evaluate the fourth derivative of the Enge funct ion at z.

double fifth(double z) const

evaluate the fifth derivative of the Enge function at z.

BLEngeType getType() const

return the type of Enge funct ion

Private Attributes

BLEngeType type

double a1

double a2

double a3
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double a4

double a5

double a6

Constructor & Destructor Documentation

BLEngeFunction::BLEngeFunction ( ) [inline]

default constructor.

References ENGE_BLOCK, and type.

00045 { type=ENGE_BLOCK; set(0,0,0,0,0,0); }

BLEngeFunction::BLEngeFunction (BLEngeType t ) [inline]

constructor for common magnet types.

References ENGE_BEND, ENGE_BLOCK, ENGE_OTHER, ENGE_QUAD, and type.

00047 {

00048 switch(t) {

00049 caseENGE_BLOCK:

00050 caseENGE_OTHER:

00051 set(0,0,0,0,0,0);

00052 break;

00053 caseENGE_BEND:

00054 set(0.478959,1.911289,-1.185953,1.630554,-1.082657,0.318111);

00055 break;

00056 caseENGE_QUAD:

00057 set(0.296471,4.533219,-2.270982,1.068627,-0.036391,0.022261);

00058 break;

00059 }00060 type= t;

00061 }

BLEngeFunction::BLEngeFunction ( double _a1,

double _a2,

double _a3,

double _a4,

double _a5,

double _a6

) [inline]

general constructor.

00064 {

00065 set(_a1,_a2,_a3,_a4,_a5,_a6);

00066 }

Member Function Documentation
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void BLEngeFunction::set ( double _a1,

double _a2,

double _a3,

double _a4,

double _a5,

double _a6

) [inline]

set the parameters.

References a1, a2, a3, a4, a5, a6, ENGE_BLOCK, ENGE_OTHER, and type.

Referenced by GenericBendField::GenericBendField(), GenericQuadField::GenericQuadField(), andMultipoleField::MultipoleField().

00069 {

00070 a1=_a1; a2=_a2; a3=_a3; a4=_a4; a5=_a5; a6=_a6;

00071 if(a1==0.0 && a2==0.0 && a3==0.0 && a4==0.0 && a5==0.0 &&

00072 a6==0.0)

00073 type= ENGE_BLOCK;

00074 else

00075 type= ENGE_OTHER;

00076 }

double BLEngeFunction::operator() ( double z) const[inline]

evaluate the Enge function at z.

References a1, a2, a3, a4, a5, a6, ENGE_BLOCK, and type.

00078 {

00079 if(type== ENGE_BLOCK) return(z 4.0) return0.0;

00082 return1.0/(1.0+exp(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*a6))))));

00083 }

double BLEngeFunction::prime ( double z) const[inline]

evaluate the derivative of the Enge function at z.


Referenced by GenericQuadField::addFieldValue(), GenericBendField::addFieldValue(), and first().

00085 {

00086 if(type== ENGE_BLOCK) return0.0;

00087 if(fabs(z) > 4.0) return0.0;

00088 doubleexp1 = exp(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*a6)))));

00089 return-exp1/(1.0+exp1)/(1.0+exp1)*

00090 (a2+z*(2.0*a3+z*(3.0*a4+z*(4.0*a5+z*5.0*a6))));

00091 }

double BLEngeFunction::first ( double z) [inline]
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References prime().

00092 { returnprime(z); }

double BLEngeFunction::second ( double z) const[inline]

evaluate the second derivative of the Enge function at z.


Referenced by GenericBendField::addFieldValue().

00094 {


00096 if(fabs(z) > 4.0) return0.0;

00097 doublef1 = a1+z*(a2+z*(a3+z*(a4+z*(a5+z*a6))));

00098 doublef2 = (a2+2*a3*z+3*a4*z*z+4*a5*z*z*z+5*a6*z*z*z*z);

00099 doublef3 = (2*a3+6*a4*z+12*a5*z*z+20*a6*z*z*z);

00100 doubleexp1 = exp(f1);

00101 returnexp1*((exp1-1.0)*f2*f2-(1.0+exp1)*f3)/

00102 (1.0+exp1)/(1.0+exp1)/(1.0+exp1);

00103 }

double BLEngeFunction::third ( double z) const[inline]

evaluate the third derivative of the Enge function at z.



00105 {

00106 if(type== ENGE_BLOCK) return0.0;00107 if(fabs(z) > 4.0) return0.0;


00109 doublef2 = a2+z*(2*a3+z*(3*a4+4*a5*z+5*a6*z*z));

00110 doublef3 = 2*(a3+z*(3*a4+2*z*(3*a5+5*a6*z)));

00111 doublef4 = a4+2.0*z*(2.0*a5+5.0*a6*z);


00113 doubleonepexp1 = 1.0 + exp1;

00114 return-exp1*(6*exp1*exp1*f2*f2*f2-6*exp1*f2*(f2*f2+f3)*onepexp1

00115 +(f2*f2*f2+3*f2*f3+6*f4)*onepexp1*onepexp1)

00116 /(onepexp1*onepexp1*onepexp1*onepexp1);

00117 }

double BLEngeFunction::fourth ( double z ) const[inline]

evaluate the fourth derivative of the Enge function at z.



00119 {


00121 if(fabs(z) > 4.0) return0.0;
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00124 doublef3 = 2*(a3+z*(3*a4+2*z*(3*a5+5*a6*z)));

00125 doublef4 = a4+2.0*z*(2.0*a5+5.0*a6*z);

00126 doublef5 = a5+ 5*a6*z;



00129 return-exp1*(-24*exp1*exp1*exp1*f2*f2*f2*f2+onepexp1*

00130 (36*exp1*exp1*f2*f2*(f2*f2+f3)-2*exp1*(7*f2*f2*f2*f2

00131 +18*f2*f2*f3+3*f3*f3+24*f2*f4)*onepexp1

00132 +(f2*f2*f2*f2+6*f2*f2*f3+3*f3*f3+24*f2*f4+24*f5)00133 *onepexp1*onepexp1))

00134 /(onepexp1*onepexp1*onepexp1*onepexp1*onepexp1);

00135 }

double BLEngeFunction::fifth ( double z) const[inline]

evaluate the fifth derivative of the Enge function at z.



00137 {


00139 if(fabs(z) > 4.0) return0.0;



00142 doublef3 = 2*(a3+z*(3*a4+2*z*(3*a5+5*a6*z)));

00143 doublef4 = a4+2.0*z*(2.0*a5+5.0*a6*z);

00144 doublef5 = a5+ 5*a6*z;



00147 return-exp1/(onepexp1*onepexp1*onepexp1*onepexp1*onepexp1*onepexp

00148 *(120*exp1*exp1*exp1*exp1*f2*f2*f2*f2*f200149 -240*exp1*exp1*exp1*f2*f2*f2*(f2*f2+f3)*onepexp1

00150 +onepexp1*onepexp1*(30*exp1*exp1*f2*(5*f2*f2*f2*f2

00151 +12*f2*f2*f3+3*f3*f3+12*f2*f4)-10*exp1*(3*f2*f2*f2*f2*f2

00152 +14*f2*f2*f2*f3+9*f2*f3*f3+36*f2*f2*f4+12*f3*f4+24*f2*f5)

00153 *onepexp1+(120*a6+f2*f2*f2*f2*f2+10*f2*f2*f2*f3+60*f2*f2*f4

00154 +60*f3*f4+15*f2*(f3*f3+8*f5))*onepexp1*onepexp1));

00155 }

BLEngeTypeBLEngeFunction::getType ( ) const[inline]

return the type of Enge function

References type.

Referenced by GenericBendField::GenericBendField(), and GenericQuadField::GenericQuadField().

00157 { returntype; }

Member Data Documentation
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BLEngeTypeBLEngeFunction::type[private]

Referenced by BLEngeFunction(), fifth(), fourth(), getType(), operator()() , prime(), second(), set(), andthird().

double BLEngeFunction::a1[private]

Referenced by fifth(), fourth(), operator()(), prime(), second(), set(), and third().











The documentation for this class was generated from the following file:

BLEngeFunction.hh

g4beamline
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g4beamline_ blengefunction class reference.pdf

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