| 1 | <html><head><meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1"><title>4.3. Electromagnetic Field</title><link rel="stylesheet" href="../xml/XSLCustomizationLayer/G4HTMLStylesheet.css" type="text/css"><meta name="generator" content="DocBook XSL Stylesheets V1.71.1"><link rel="start" href="index.html" title="Geant4 User's Guide for Application Developers"><link rel="up" href="ch04.html" title="Chapter 4. Detector Definition and Response"><link rel="prev" href="ch04s02.html" title="4.2. Material"><link rel="next" href="ch04s04.html" title="4.4. Hits"><script language="JavaScript">
|
|---|
| 2 | function remote_win(fName)
|
|---|
| 3 | {
|
|---|
| 4 | var url = "AllResources/Detector/geometry.src/" + fName;
|
|---|
| 5 | RemoteWin=window.open(url,"","resizable=no,toolbar=0,location=0,directories=0,status=0,menubar=0,scrollbars=0,copyhistory=0,width=520,height=520")
|
|---|
| 6 | RemoteWin.creator=self
|
|---|
| 7 | }
|
|---|
| 8 | </script></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">4.3.
|
|---|
| 9 | Electromagnetic Field
|
|---|
| 10 | </th></tr><tr><td width="20%" align="left"><a accesskey="p" href="ch04s02.html"><img src="AllResources/IconsGIF/prev.gif" alt="Prev"></a> </td><th width="60%" align="center">Chapter 4.
|
|---|
| 11 | Detector Definition and Response
|
|---|
| 12 | </th><td width="20%" align="right"> <a accesskey="n" href="ch04s04.html"><img src="AllResources/IconsGIF/next.gif" alt="Next"></a></td></tr></table><hr></div><div class="sect1" lang="en"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="sect.EMField"></a>4.3.
|
|---|
| 13 | Electromagnetic Field
|
|---|
| 14 | </h2></div></div></div><div class="sect2" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="sect.EMField.Overview"></a>4.3.1.
|
|---|
| 15 | An Overview of Propagation in a Field
|
|---|
| 16 | </h3></div></div></div><p>
|
|---|
| 17 | Geant4 is capable of describing and propagating in a variety of
|
|---|
| 18 | fields. Magnetic fields, electric fields and electromagnetic,
|
|---|
| 19 | uniform or non-uniform, can specified for a Geant4 setup. The
|
|---|
| 20 | propagation of tracks inside them can be performed to a
|
|---|
| 21 | user-defined accuracy.
|
|---|
| 22 | </p><p>
|
|---|
| 23 | In order to propagate a track inside a field, the equation of
|
|---|
| 24 | motion of the particle in the field is integrated. In general, this
|
|---|
| 25 | is done using a Runge-Kutta method for the integration of ordinary
|
|---|
| 26 | differential equations. However, for specific cases where an
|
|---|
| 27 | analytical solution is known, it is possible to utilize this
|
|---|
| 28 | instead. Several Runge-Kutta methods are available, suitable for
|
|---|
| 29 | different conditions. In specific cases (such as a uniform field
|
|---|
| 30 | where the analytical solution is known) different solvers can also
|
|---|
| 31 | be used. In addition, when an approximate analytical solution is
|
|---|
| 32 | known, it is possible to utilize it in an iterative manner in order
|
|---|
| 33 | to converge to the solution to the precision required. This latter
|
|---|
| 34 | method is currently implemented and can be used particularly well
|
|---|
| 35 | for magnetic fields that are almost uniform.
|
|---|
| 36 | </p><p>
|
|---|
| 37 | Once a method is chosen that calculates the track's propagation
|
|---|
| 38 | in a specific field, the curved path is broken up into linear chord
|
|---|
| 39 | segments. These chord segments are determined so that they closely
|
|---|
| 40 | approximate the curved path. The chords are then used to
|
|---|
| 41 | interrogate the Navigator as to whether the track has crossed a
|
|---|
| 42 | volume boundary. Several parameters are available to adjust the
|
|---|
| 43 | accuracy of the integration and the subsequent interrogation of the
|
|---|
| 44 | model geometry.
|
|---|
| 45 | </p><p>
|
|---|
| 46 | How closely the set of chords approximates a curved trajectory
|
|---|
| 47 | is governed by a parameter called the <span class="emphasis"><em>miss distance</em></span> (also
|
|---|
| 48 | called the <span class="emphasis"><em>chord distance</em></span> ). This is an upper bound for the
|
|---|
| 49 | value of the sagitta - the distance between the 'real' curved
|
|---|
| 50 | trajectory and the approximate linear trajectory of the chord. By
|
|---|
| 51 | setting this parameter, the user can control the precision of the
|
|---|
| 52 | volume interrogation. Every attempt has been made to ensure that
|
|---|
| 53 | all volume interrogations will be made to an accuracy within this
|
|---|
| 54 | <span class="emphasis"><em>miss distance</em></span>.
|
|---|
| 55 |
|
|---|
| 56 | </p><div class="figure"><a name="fig.EMField_1"></a><div class="figure-contents"><div class="mediaobject" align="center"><img src="./AllResources/Detector/electroMagneticField.src/MissDistance.jpg" align="middle" alt="Miss Distance"></div></div><p class="title"><b>Figure 4.6.
|
|---|
| 57 | The curved trajectory will be approximated by chords,
|
|---|
| 58 | so that the maximum estimated distance between curve and chord is
|
|---|
| 59 | less than the the <span class="emphasis"><em>miss distance</em></span>.
|
|---|
| 60 | </b></p></div><p><br class="figure-break">
|
|---|
| 61 | </p><p>
|
|---|
| 62 | In addition to the <span class="emphasis"><em>miss distance</em></span> there are two more
|
|---|
| 63 | parameters which the user can set in order to adjust the accuracy
|
|---|
| 64 | (and performance) of tracking in a field. In particular these
|
|---|
| 65 | parameters govern the accuracy of the intersection with a volume
|
|---|
| 66 | boundary and the accuracy of the integration of other steps. As
|
|---|
| 67 | such they play an important role for tracking.
|
|---|
| 68 | </p><p>
|
|---|
| 69 | The <span class="emphasis"><em>delta intersection</em></span> parameter is the accuracy to which
|
|---|
| 70 | an intersection with a volume boundary is calculated. If a
|
|---|
| 71 | candidate boundary intersection is estimated to have a precision
|
|---|
| 72 | better than this, it is accepted. This parameter is especially
|
|---|
| 73 | important because it is used to limit a bias that our algorithm
|
|---|
| 74 | (for boundary crossing in a field) exhibits. This algorithm
|
|---|
| 75 | calculates the intersection with a volume boundary using a chord
|
|---|
| 76 | between two points on the curved particle trajectory. As such, the
|
|---|
| 77 | intersection point is always on the 'inside' of the curve. By
|
|---|
| 78 | setting a value for this parameter that is much smaller than some
|
|---|
| 79 | acceptable error, the user can limit the effect of this bias on,
|
|---|
| 80 | for example, the future estimation of the reconstructed particle
|
|---|
| 81 | momentum.
|
|---|
| 82 |
|
|---|
| 83 | </p><div class="figure"><a name="fig.EMField_2"></a><div class="figure-contents"><div class="mediaobject" align="center"><img src="./AllResources/Detector/electroMagneticField.src/IntersectionError.jpg" align="middle" alt="Figure: The distance between the calculated chord intersection point and a computed curve point."></div></div><p class="title"><b>Figure 4.7.
|
|---|
| 84 | The distance between the calculated chord intersection
|
|---|
| 85 | point C and a computed curve point D is used to determine whether C
|
|---|
| 86 | is an accurate representation of the intersection of the curved
|
|---|
| 87 | path ADB with a volume boundary. Here CD is likely too large, and a
|
|---|
| 88 | new intersection on the chord AD will be calculated.
|
|---|
| 89 | </b></p></div><p><br class="figure-break">
|
|---|
| 90 | </p><p>
|
|---|
| 91 | The <span class="emphasis"><em>delta one step</em></span> parameter is the accuracy for the
|
|---|
| 92 | endpoint of 'ordinary' integration steps, those which do not
|
|---|
| 93 | intersect a volume boundary. This parameter is a limit on the
|
|---|
| 94 | estimated error of the endpoint of each physics step. It can be
|
|---|
| 95 | seen as akin to a statistical uncertainty and is not expected to
|
|---|
| 96 | contribute any systematic behavior to physical quantities. In
|
|---|
| 97 | contrast, the bias addressed by <span class="emphasis"><em>delta intersection</em></span> is
|
|---|
| 98 | clearly correlated with potential systematic errors in the momentum
|
|---|
| 99 | of reconstructed tracks. Thus very strict limits on the
|
|---|
| 100 | intersection parameter should be used in tracking detectors or
|
|---|
| 101 | wherever the intersections are used to reconstruct a track's
|
|---|
| 102 | momentum.
|
|---|
| 103 | </p><p>
|
|---|
| 104 | <span class="emphasis"><em>Delta intersection</em></span> and <span class="emphasis"><em>delta one step</em></span> are
|
|---|
| 105 | parameters of the Field Manager; the user can set them according to
|
|---|
| 106 | the demands of his application. Because it is possible to use more
|
|---|
| 107 | than one field manager, different values can be set for different
|
|---|
| 108 | detector regions.
|
|---|
| 109 | </p><p>
|
|---|
| 110 | Note that reasonable values for the two parameters are strongly
|
|---|
| 111 | coupled: it does not make sense to request an accuracy of 1 nm for
|
|---|
| 112 | <span class="emphasis"><em>delta intersection</em></span> and accept 100 &#956m for the
|
|---|
| 113 | <span class="emphasis"><em>delta one step</em></span> error value. Nevertheless <span class="emphasis"><em>delta
|
|---|
| 114 | intersection</em></span> is the more important of the two. It is
|
|---|
| 115 | recommended that these parameters should not differ significantly -
|
|---|
| 116 | certainly not by more than an order of magnitude.
|
|---|
| 117 | </p></div><div class="sect2" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="sect.EMField.Pract"></a>4.3.2.
|
|---|
| 118 | Practical Aspects
|
|---|
| 119 | </h3></div></div></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.EMField.Pract.MagField"></a>4.3.2.1.
|
|---|
| 120 | Creating a Magnetic Field for a Detector
|
|---|
| 121 | </h4></div></div></div><p>
|
|---|
| 122 | The simplest way to define a field for a detector involves the
|
|---|
| 123 | following steps:
|
|---|
| 124 |
|
|---|
| 125 | </p><div class="orderedlist"><ol type="1" compact><li><p>
|
|---|
| 126 | create a field:
|
|---|
| 127 | </p><div class="informalexample"><pre class="programlisting">
|
|---|
| 128 | G4UniformMagField* magField
|
|---|
| 129 | = new G4UniformMagField(G4ThreeVector(0.,0.,fieldValue));
|
|---|
| 130 | </pre></div><p>
|
|---|
| 131 | </p></li><li><p>
|
|---|
| 132 | set it as the default field:
|
|---|
| 133 | </p><div class="informalexample"><pre class="programlisting">
|
|---|
| 134 | G4FieldManager* fieldMgr
|
|---|
| 135 | = G4TransportationManager::GetTransportationManager()
|
|---|
| 136 | ->GetFieldManager();
|
|---|
| 137 | fieldMgr->SetDetectorField(magField);
|
|---|
| 138 | </pre></div><p>
|
|---|
| 139 | </p></li><li><p>
|
|---|
| 140 | create the objects which calculate the trajectory:
|
|---|
| 141 | </p><div class="informalexample"><pre class="programlisting">
|
|---|
| 142 | fieldMgr->CreateChordFinder(magField);
|
|---|
| 143 | </pre></div><p>
|
|---|
| 144 | </p></li></ol></div><p>
|
|---|
| 145 | </p><p>
|
|---|
| 146 | To change the accuracy of volume intersection use the
|
|---|
| 147 | <code class="literal">SetDeltaChord</code> method:
|
|---|
| 148 |
|
|---|
| 149 | </p><div class="informalexample"><pre class="programlisting">
|
|---|
| 150 | fieldMgr->GetChordFinder()->SetDeltaChord( G4double newValue);
|
|---|
| 151 | </pre></div><p>
|
|---|
| 152 | </p></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.EMField.Pract.PartVol"></a>4.3.2.2.
|
|---|
| 153 | Creating a Field for a Part of the Volume Hierarchy
|
|---|
| 154 | </h4></div></div></div><p>
|
|---|
| 155 | It is possible to create a field for a part of the detector. In
|
|---|
| 156 | particular it can describe the field (with pointer fEmField, for
|
|---|
| 157 | example) inside a logical volume and all its daughters. This can be
|
|---|
| 158 | done by simply creating a <code class="literal">G4FieldManager</code> and attaching it
|
|---|
| 159 | to a logical volume (with pointer, logicVolumeWithField, for
|
|---|
| 160 | example) or set of logical volumes.
|
|---|
| 161 |
|
|---|
| 162 | </p><div class="informalexample"><pre class="programlisting">
|
|---|
| 163 | G4bool allLocal = true;
|
|---|
| 164 | logicVolumeWithField->SetFieldManager(localFieldManager, allLocal);
|
|---|
| 165 | </pre></div><p>
|
|---|
| 166 | </p><p>
|
|---|
| 167 | Using the second parameter to <code class="literal">SetFieldManager</code> you choose
|
|---|
| 168 | whether daughter volumes of this logical volume will also be given this new
|
|---|
| 169 | field. If it has the value <code class="literal">true</code>, the field will be
|
|---|
| 170 | assigned also to its daughters, and all their sub-volumes.
|
|---|
| 171 | Else, if it is <code class="literal">false</code>, it will be copied only to those
|
|---|
| 172 | daughter volumes which do not have a field manager already.
|
|---|
| 173 | </p></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.EMField.Pract.Electric"></a>4.3.2.3.
|
|---|
| 174 | Creating an Electric or Electromagnetic Field
|
|---|
| 175 | </h4></div></div></div><p>
|
|---|
| 176 | The design and implementation of the <span class="emphasis"><em>Field</em></span> category
|
|---|
| 177 | allows and enables the use of an electric or combined
|
|---|
| 178 | electromagnetic field. These fields can also vary with time, as can
|
|---|
| 179 | magnetic fields.
|
|---|
| 180 | </p><p>
|
|---|
| 181 | Source listing <a href="ch04s03.html#programlist_EMField_1" title="Example 4.12.
|
|---|
| 182 | How to define a uniform electric field for the whole of a detector,
|
|---|
| 183 | extracted from example in examples/extended/field/field02 .
|
|---|
| 184 | ">Example 4.12</a> shows how to
|
|---|
| 185 | define a uniform electric field for the whole of a detector.
|
|---|
| 186 |
|
|---|
| 187 | </p><div class="example"><a name="programlist_EMField_1"></a><p class="title"><b>Example 4.12.
|
|---|
| 188 | How to define a uniform electric field for the whole of a detector,
|
|---|
| 189 | extracted from example in examples/extended/field/field02 .
|
|---|
| 190 | </b></p><div class="example-contents"><pre class="programlisting">
|
|---|
| 191 | // in the header file (or first)
|
|---|
| 192 | #include "G4EqMagElectricField.hh"
|
|---|
| 193 | #include "G4UniformElectricField.hh"
|
|---|
| 194 |
|
|---|
| 195 | ...
|
|---|
| 196 | G4ElectricField* fEMfield;
|
|---|
| 197 | G4EqMagElectricField* fEquation;
|
|---|
| 198 | G4MagIntegratorStepper* fStepper;
|
|---|
| 199 | G4FieldManager* fFieldMgr;
|
|---|
| 200 | G4double fMinStep ;
|
|---|
| 201 | G4ChordFinder* fChordFinder ;
|
|---|
| 202 |
|
|---|
| 203 | // in the source file
|
|---|
| 204 |
|
|---|
| 205 | {
|
|---|
| 206 | fEMfield = new G4UniformElectricField(
|
|---|
| 207 | G4ThreeVector(0.0,100000.0*kilovolt/cm,0.0));
|
|---|
| 208 |
|
|---|
| 209 | // Create an equation of motion for this field
|
|---|
| 210 | fEquation = new G4EqMagElectricField(fEMfield);
|
|---|
| 211 |
|
|---|
| 212 | G4int nvar = 8;
|
|---|
| 213 | fStepper = new G4ClassicalRK4( fEquation, nvar );
|
|---|
| 214 |
|
|---|
| 215 | // Get the global field manager
|
|---|
| 216 | fFieldManager= G4TransportationManager::GetTransportationManager()->
|
|---|
| 217 | GetFieldManager();
|
|---|
| 218 | // Set this field to the global field manager
|
|---|
| 219 | fFieldManager->SetDetectorField(fEMfield );
|
|---|
| 220 |
|
|---|
| 221 | fMinStep = 0.010*mm ; // minimal step of 10 microns
|
|---|
| 222 |
|
|---|
| 223 | fIntgrDriver = new G4MagInt_Driver(fMinStep,
|
|---|
| 224 | fStepper,
|
|---|
| 225 | fStepper->GetNumberOfVariables() );
|
|---|
| 226 |
|
|---|
| 227 | fChordFinder = new G4ChordFinder(fIntgrDriver);
|
|---|
| 228 | fFieldManager->SetChordFinder( fChordFinder );
|
|---|
| 229 |
|
|---|
| 230 | }
|
|---|
| 231 | </pre></div></div><p><br class="example-break">
|
|---|
| 232 | </p><p>
|
|---|
| 233 | An example with an electric field is
|
|---|
| 234 | examples/extended/field/field02, where the class
|
|---|
| 235 | F02ElectricFieldSetup demonstrates how to set these and other
|
|---|
| 236 | parameters, and how to choose different Integration Steppers.
|
|---|
| 237 | </p><p>
|
|---|
| 238 | The user can also create their own type of field, inheriting from
|
|---|
| 239 | <code class="literal">G4VField</code>, and an associated Equation of Motion class
|
|---|
| 240 | (inheriting from <code class="literal">G4EqRhs</code>) to simulate other types of
|
|---|
| 241 | fields.
|
|---|
| 242 | </p></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.EMField.Pract.Stepper"></a>4.3.2.4.
|
|---|
| 243 | Choosing a Stepper
|
|---|
| 244 | </h4></div></div></div><p>
|
|---|
| 245 | Runge-Kutta integration is used to compute the motion of a
|
|---|
| 246 | charged track in a general field. There are many general steppers
|
|---|
| 247 | from which to choose, of low and high order, and specialized
|
|---|
| 248 | steppers for pure magnetic fields. By default, Geant4 uses the
|
|---|
| 249 | classical fourth-order Runge-Kutta stepper, which is general
|
|---|
| 250 | purpose and robust. If the field is known to have specific
|
|---|
| 251 | properties, lower or higher order steppers can be used to obtain
|
|---|
| 252 | the same quality results using fewer computing cycles.
|
|---|
| 253 | </p><p>
|
|---|
| 254 | In particular, if the field is calculated from a field map, a
|
|---|
| 255 | lower order stepper is recommended. The less smooth the field is,
|
|---|
| 256 | the lower the order of the stepper that should be used. The choice
|
|---|
| 257 | of lower order steppers includes the third order stepper
|
|---|
| 258 | <code class="literal">G4SimpleHeum</code>, the second order <code class="literal">G4ImplicitEuler</code>
|
|---|
| 259 | and <code class="literal">G4SimpleRunge</code>, and the first order
|
|---|
| 260 | <code class="literal">G4ExplicitEuler</code>. A first order stepper would be useful
|
|---|
| 261 | only for very rough fields. For somewhat smooth fields
|
|---|
| 262 | (intermediate), the choice between second and third order steppers
|
|---|
| 263 | should be made by trial and error. Trying a few different types of
|
|---|
| 264 | steppers for a particular field or application is suggested if
|
|---|
| 265 | maximum performance is a goal.
|
|---|
| 266 | </p><p>
|
|---|
| 267 | The choice of stepper depends on the type of field: magnetic or
|
|---|
| 268 | general. A general field can be an electric or electromagnetic
|
|---|
| 269 | field, it can be a magnetic field or a user-defined field (which
|
|---|
| 270 | requires a user-defined equation of motion.) For a general field
|
|---|
| 271 | several steppers are available as alternatives to the default
|
|---|
| 272 | (<code class="literal">G4ClassicalRK4</code>):
|
|---|
| 273 |
|
|---|
| 274 | </p><div class="informalexample"><pre class="programlisting">
|
|---|
| 275 | G4int nvar = 8; // To integrate time & energy
|
|---|
| 276 | // in addition to position, momentum
|
|---|
| 277 | G4EqMagElectricField* fEquation= new G4EqMagElectricField(fEMfield);
|
|---|
| 278 |
|
|---|
| 279 | fStepper = new G4SimpleHeum( fEquation, nvar );
|
|---|
| 280 | // 3rd order, a good alternative to ClassicalRK
|
|---|
| 281 | fStepper = new G4SimpleRunge( fEquation, nvar );
|
|---|
| 282 | // 2nd order, for less smooth fields
|
|---|
| 283 | fStepper = new G4CashKarpRKF45( fEquation );
|
|---|
| 284 | // 4/5th order for very smooth fields
|
|---|
| 285 | </pre></div><p>
|
|---|
| 286 | </p><p>
|
|---|
| 287 | Specialized steppers for pure magnetic fields are also
|
|---|
| 288 | available. They take into account the fact that a local trajectory
|
|---|
| 289 | in a slowly varying field will not vary significantly from a helix.
|
|---|
| 290 | Combining this in with a variation the Runge-Kutta method can
|
|---|
| 291 | provide higher accuracy at lower computational cost when large
|
|---|
| 292 | steps are possible.
|
|---|
| 293 |
|
|---|
| 294 | </p><div class="informalexample"><pre class="programlisting">
|
|---|
| 295 | G4Mag_UsualEqRhs*
|
|---|
| 296 | fEquation = new G4Mag_UsualEqRhs(fMagneticField);
|
|---|
| 297 | fStepper = new G4HelixImplicitEuler( fEquation );
|
|---|
| 298 | // Note that for magnetic field that do not vary with time,
|
|---|
| 299 | // the default number of variables suffices.
|
|---|
| 300 |
|
|---|
| 301 | // or ..
|
|---|
| 302 | fStepper = new G4HelixExplicitEuler( fEquation );
|
|---|
| 303 | fStepper = new G4HelixSimpleRunge( fEquation );
|
|---|
| 304 | </pre></div><p>
|
|---|
| 305 | </p><p>
|
|---|
| 306 | You can choose an alternative stepper either when the field
|
|---|
| 307 | manager is constructed or later. At the construction of the
|
|---|
| 308 | ChordFinder it is an optional argument:
|
|---|
| 309 |
|
|---|
| 310 | </p><div class="informalexample"><pre class="programlisting">
|
|---|
| 311 | G4ChordFinder( G4MagneticField* itsMagField,
|
|---|
| 312 | G4double stepMinimum = 1.0e-2 * mm,
|
|---|
| 313 | G4MagIntegratorStepper* pItsStepper = 0 );
|
|---|
| 314 | </pre></div><p>
|
|---|
| 315 | </p><p>
|
|---|
| 316 | To change the stepper at a later time use
|
|---|
| 317 |
|
|---|
| 318 | </p><div class="informalexample"><pre class="programlisting">
|
|---|
| 319 | pChordFinder->GetIntegrationDriver()
|
|---|
| 320 | ->RenewStepperAndAdjust( newStepper );
|
|---|
| 321 | </pre></div><p>
|
|---|
| 322 | </p></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.EMField.Pract.Adjust"></a>4.3.2.5.
|
|---|
| 323 | How to Adjust the Accuracy of Propagation
|
|---|
| 324 | </h4></div></div></div><p>
|
|---|
| 325 | In order to obtain a particular accuracy in tracking particles
|
|---|
| 326 | through an electromagnetic field, it is necessary to adjust the
|
|---|
| 327 | parameters of the field propagation module. In the following
|
|---|
| 328 | section, some of these additional parameters are discussed.
|
|---|
| 329 | </p><p>
|
|---|
| 330 | When integration is used to calculate the trajectory, it is
|
|---|
| 331 | necessary to determine an acceptable level of numerical imprecision
|
|---|
| 332 | in order to get performant simulation with acceptable errors. The
|
|---|
| 333 | parameters in Geant4 tell the field module what level of
|
|---|
| 334 | integration inaccuracy is acceptable.
|
|---|
| 335 | </p><p>
|
|---|
| 336 | In all quantities which are integrated (position, momentum,
|
|---|
| 337 | energy) there will be errors. Here, however, we focus on the error
|
|---|
| 338 | in two key quantities: the position and the momentum. (The error in
|
|---|
| 339 | the energy will come from the momentum integration).
|
|---|
| 340 | </p><p>
|
|---|
| 341 | Three parameters exist which are relevant to the integration
|
|---|
| 342 | accuracy. DeltaOneStep is a distance and is roughly the position
|
|---|
| 343 | error which is acceptable in an integration step. Since many
|
|---|
| 344 | integration steps may be required for a single physics step,
|
|---|
| 345 | DeltaOneStep should be a fraction of the average physics step size.
|
|---|
| 346 | The next two parameters impose a further limit on the relative
|
|---|
| 347 | error of the position/momentum inaccuracy. EpsilonMin and
|
|---|
| 348 | EpsilonMax impose a minimum and maximum on this relative error -
|
|---|
| 349 | and take precedence over DeltaOneStep. (Note: if you set
|
|---|
| 350 | EpsilonMin=EpsilonMax=your-value, then all steps will be made to
|
|---|
| 351 | this relative precision.
|
|---|
| 352 |
|
|---|
| 353 | </p><div class="example"><a name="programlist_EMField_2"></a><p class="title"><b>Example 4.13.
|
|---|
| 354 | How to set accuracy parameters for the 'global' field of the setup.
|
|---|
| 355 | </b></p><div class="example-contents"><pre class="programlisting">
|
|---|
| 356 | G4FieldManager *globalFieldManager;
|
|---|
| 357 |
|
|---|
| 358 | G4TransportationManager *transportMgr=
|
|---|
| 359 | G4TransportationManager::GetTransportationManager();
|
|---|
| 360 |
|
|---|
| 361 | globalFieldManager = transportMgr->GetFieldManager();
|
|---|
| 362 | // Relative accuracy values:
|
|---|
| 363 | G4double minEps= 1.0e-5; // Minimum & value for smallest steps
|
|---|
| 364 | G4double maxEps= 1.0e-4; // Maximum & value for largest steps
|
|---|
| 365 |
|
|---|
| 366 | globalFieldManager->SetMinimumEpsilonStep( minEps );
|
|---|
| 367 | globalFieldManager->SetMaximumEpsilonStep( maxEps );
|
|---|
| 368 | globalFieldManager->SetDeltaOneStep( 0.5e-3 * mm ); // 0.5 micrometer
|
|---|
| 369 |
|
|---|
| 370 | G4cout << "EpsilonStep: set min= " << minEps << " max= " << maxEps << G4endl;
|
|---|
| 371 | </pre></div></div><p><br class="example-break">
|
|---|
| 372 | </p><p>
|
|---|
| 373 | We note that the relevant parameters above limit the inaccuracy
|
|---|
| 374 | in each step. The final inaccuracy due to the full trajectory will
|
|---|
| 375 | accumulate!
|
|---|
| 376 | </p><p>
|
|---|
| 377 | The exact point at which a track crosses a boundary is also
|
|---|
| 378 | calculated with finite accuracy. To limit this inaccuracy, a
|
|---|
| 379 | parameter called DeltaIntersection is used. This is a maximum for
|
|---|
| 380 | the inaccuracy of a single boundary crossing. Thus the accuracy of
|
|---|
| 381 | the position of the track after a number of boundary crossings is
|
|---|
| 382 | directly proportional to the number of boundaries.
|
|---|
| 383 | </p></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.EMField.Pract.DiffAcc"></a>4.3.2.6.
|
|---|
| 384 | Choosing different accuracies for the same volume
|
|---|
| 385 | </h4></div></div></div><p>
|
|---|
| 386 | It is possible to create a FieldManager which has different
|
|---|
| 387 | properties for particles of different momenta (or depending on
|
|---|
| 388 | other parameters of a track). This is useful, for example, in
|
|---|
| 389 | obtaining high accuracy for 'important' tracks (e.g. muons) and
|
|---|
| 390 | accept less accuracy in tracking others (e.g. electrons). To use
|
|---|
| 391 | this, you must create your own field manager which uses the
|
|---|
| 392 | method
|
|---|
| 393 |
|
|---|
| 394 | </p><div class="informalexample"><pre class="programlisting">
|
|---|
| 395 | void ConfigureForTrack( const G4Track * );
|
|---|
| 396 | </pre></div><p>
|
|---|
| 397 |
|
|---|
| 398 | to configure itself using the parameters of the current track.
|
|---|
| 399 | An example of this will be available in
|
|---|
| 400 | examples/extended/field05.
|
|---|
| 401 | </p></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.EMField.Pract.ParaScal"></a>4.3.2.7.
|
|---|
| 402 | Parameters that must scale with problem size
|
|---|
| 403 | </h4></div></div></div><p>
|
|---|
| 404 | The default settings of this module are for problems with the
|
|---|
| 405 | physical size of a typical high energy physics setup, that is,
|
|---|
| 406 | distances smaller than about one kilometer. A few parameters are
|
|---|
| 407 | necessary to carry this information to the magnetic field module,
|
|---|
| 408 | and must typically be rescaled for problems of vastly different
|
|---|
| 409 | sizes in order to get reasonable performance and robustness. Two of
|
|---|
| 410 | these parameters are the maximum acceptable step and the minimum
|
|---|
| 411 | step size.
|
|---|
| 412 | </p><p>
|
|---|
| 413 | The <span class="bold"><strong>maximum acceptable step</strong></span> should be set
|
|---|
| 414 | to a distance larger than the biggest reasonable step. If the apparatus
|
|---|
| 415 | in a setup has a diameter of two meters, a likely maximum acceptable
|
|---|
| 416 | steplength would be 10 meters. A particle could then take large
|
|---|
| 417 | spiral steps, but would not attempt to take, for example, a
|
|---|
| 418 | 1000-meter-long step in the case of a very low-density material.
|
|---|
| 419 | Similarly, for problems of a planetary scale, such as the earth
|
|---|
| 420 | with its radius of roughly 6400 km, a maximum acceptabe steplength
|
|---|
| 421 | of a few times this value would be reasonable.
|
|---|
| 422 | </p><p>
|
|---|
| 423 | An upper limit for the size of a step is a parameter of
|
|---|
| 424 | <code class="literal">G4PropagatorInField</code>, and can be set by calling its
|
|---|
| 425 | <code class="literal">SetLargestAcceptableStep</code> method.
|
|---|
| 426 | </p><p>
|
|---|
| 427 | The <span class="bold"><strong>minimum step size</strong></span> is used during
|
|---|
| 428 | integration to limit the amount of work in difficult cases. It is
|
|---|
| 429 | possible that strong fields or integration problems can force the
|
|---|
| 430 | integrator to try very small steps; this parameter stops them from
|
|---|
| 431 | becoming unnecessarily small.
|
|---|
| 432 | </p><p>
|
|---|
| 433 | Trial steps smaller than this parameter will be treated with
|
|---|
| 434 | less accuracy, and may even be ignored, depending on the
|
|---|
| 435 | situation.
|
|---|
| 436 | </p><p>
|
|---|
| 437 | The minimum step size is a parameter of the MagInt_Driver, but
|
|---|
| 438 | can be set in the contstructor of G4ChordFinder, as in the source
|
|---|
| 439 | listing above.
|
|---|
| 440 | </p></div><div class="sect3" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="sect.EMField.Pract.Known"></a>4.3.2.8.
|
|---|
| 441 | Known Issues
|
|---|
| 442 | </h4></div></div></div><p>
|
|---|
| 443 | Currently it is computationally expensive to change the <span class="emphasis"><em>miss
|
|---|
| 444 | distance</em></span> to very small values, as it causes tracks to be
|
|---|
| 445 | limited to curved sections whose 'bend' is smaller than this value.
|
|---|
| 446 | (The bend is the distance of the mid-point from the chord between
|
|---|
| 447 | endpoints.) For tracks with small curvature (typically low momentum
|
|---|
| 448 | particles in strong fields) this can cause a large number of
|
|---|
| 449 | steps
|
|---|
| 450 |
|
|---|
| 451 | </p><div class="itemizedlist"><ul type="disc" compact><li><p>
|
|---|
| 452 | even in areas where there are no volumes to intersect
|
|---|
| 453 | (something that is expected to be addressed in future development,
|
|---|
| 454 | in which the safety will be utilized to partially alleviate this
|
|---|
| 455 | limitation)
|
|---|
| 456 | </p></li><li><p>
|
|---|
| 457 | especially in a region near a volume boundary (in which case it
|
|---|
| 458 | is necessary in order to discover whether a track might intersect a
|
|---|
| 459 | volume for only a short distance.)
|
|---|
| 460 | </p></li></ul></div><p>
|
|---|
| 461 | </p><p>
|
|---|
| 462 | Requiring such precision at the intersection is clearly expensive,
|
|---|
| 463 | and new development would be necessary to minimize the expense.
|
|---|
| 464 | </p><p>
|
|---|
| 465 | By contrast, changing the intersection parameter is less
|
|---|
| 466 | computationally expensive. It causes further calculation for only a
|
|---|
| 467 | fraction of the steps, in particular those that intersect a volume
|
|---|
| 468 | boundary.
|
|---|
| 469 | </p></div></div><div class="sect2" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="sect.EMField.Spin"></a>4.3.3.
|
|---|
| 470 | Spin Tracking
|
|---|
| 471 | </h3></div></div></div><p>
|
|---|
| 472 | The effects of a particle's motion on the precession of its spin
|
|---|
| 473 | angular momentum in slowly varying external fields are simulated.
|
|---|
| 474 | The relativistic equation of motion for spin is known as the BMT
|
|---|
| 475 | equation. The equation demonstrates a remarkable property; in a
|
|---|
| 476 | purely magnetic field, in vacuum, and neglecting small anomalous
|
|---|
| 477 | magnetic moments, the particle's spin precesses in such a manner
|
|---|
| 478 | that the longitudinal polarization remains a constant, whatever the
|
|---|
| 479 | motion of the particle. But when the particle interacts with
|
|---|
| 480 | electric fields of the medium and multiple scatters, the spin,
|
|---|
| 481 | which is related to the particle's magnetic moment, does not
|
|---|
| 482 | participate, and the need thus arises to propagate it independent
|
|---|
| 483 | of the momentum vector. In the case of a polarized muon beam, for
|
|---|
| 484 | example, it is important to predict the muon's spin direction at
|
|---|
| 485 | decay-time in order to simulate the decay electron (Michel)
|
|---|
| 486 | distribution correctly.
|
|---|
| 487 | </p><p>
|
|---|
| 488 | In order to track the spin of a particle in a magnetic field,
|
|---|
| 489 | you need to code the following:
|
|---|
| 490 |
|
|---|
| 491 | </p><div class="orderedlist"><ol type="1" compact><li><p>
|
|---|
| 492 | in your DetectorConstruction
|
|---|
| 493 |
|
|---|
| 494 | </p><div class="informalexample"><pre class="programlisting">
|
|---|
| 495 | #include "G4Mag_SpinEqRhs.hh"
|
|---|
| 496 |
|
|---|
| 497 | G4Mag_EqRhs* fEquation = new G4Mag_SpinEqRhs(magField);
|
|---|
| 498 |
|
|---|
| 499 | G4MagIntegratorStepper* pStepper = new G4ClassicalRK4(fEquation,12);
|
|---|
| 500 | <span class="bold"><strong>notice the 12 </strong></span>
|
|---|
| 501 | </pre></div><p>
|
|---|
| 502 | </p></li><li><p>
|
|---|
| 503 | in your PrimaryGenerator
|
|---|
| 504 |
|
|---|
| 505 | </p><div class="informalexample"><pre class="programlisting">
|
|---|
| 506 | particleGun->SetParticlePolarization(G4ThreeVector p)
|
|---|
| 507 | </pre></div><p>
|
|---|
| 508 |
|
|---|
| 509 | for example:
|
|---|
| 510 |
|
|---|
| 511 | </p><div class="informalexample"><pre class="programlisting">
|
|---|
| 512 | particleGun->
|
|---|
| 513 | SetParticlePolarization(-(particleGun->GetParticleMomentumDirection()));
|
|---|
| 514 |
|
|---|
| 515 | // or
|
|---|
| 516 | particleGun->
|
|---|
| 517 | SetParticlePolarization(particleGun->GetParticleMomentumDirection()
|
|---|
| 518 | .cross(G4ThreeVector(0.,1.,0.)));
|
|---|
| 519 | </pre></div><p>
|
|---|
| 520 |
|
|---|
| 521 | where you set the initial spin direction.
|
|---|
| 522 | </p></li></ol></div><p>
|
|---|
| 523 | </p><p>
|
|---|
| 524 | While the G4Mag_SpinEqRhs class constructor
|
|---|
| 525 |
|
|---|
| 526 | </p><div class="informalexample"><pre class="programlisting">
|
|---|
| 527 | G4Mag_SpinEqRhs::G4Mag_SpinEqRhs( G4MagneticField* MagField )
|
|---|
| 528 | : G4Mag_EqRhs( MagField )
|
|---|
| 529 | {
|
|---|
| 530 | anomaly = 1.165923e-3;
|
|---|
| 531 | }
|
|---|
| 532 | </pre></div><p>
|
|---|
| 533 |
|
|---|
| 534 | sets the muon anomaly by default, the class also comes with the
|
|---|
| 535 | public method:
|
|---|
| 536 |
|
|---|
| 537 | </p><div class="informalexample"><pre class="programlisting">
|
|---|
| 538 | inline void SetAnomaly(G4double a) { anomaly = a; }
|
|---|
| 539 | </pre></div><p>
|
|---|
| 540 |
|
|---|
| 541 | with which you can set the magnetic anomaly to any value you
|
|---|
| 542 | require.
|
|---|
| 543 | </p><p>
|
|---|
| 544 | For the moment, the code is written such that field tracking of
|
|---|
| 545 | the spin is done only for particles with non-zero charge. Please,
|
|---|
| 546 | see the Forum posting:
|
|---|
| 547 |
|
|---|
| 548 | <code class="literal">
|
|---|
| 549 | http://geant4-hn.slac.stanford.edu:5090/HyperNews/public/get/emfields/88/3/1.html
|
|---|
| 550 | </code>
|
|---|
| 551 |
|
|---|
| 552 | for modifications the user is required to make to facilitate
|
|---|
| 553 | neutron spin tracking.
|
|---|
| 554 | </p></div></div><div class="navfooter"><hr><table width="100%" summary="Navigation footer"><tr><td width="40%" align="left"><a accesskey="p" href="ch04s02.html"><img src="AllResources/IconsGIF/prev.gif" alt="Prev"></a> </td><td width="20%" align="center"><a accesskey="u" href="ch04.html"><img src="AllResources/IconsGIF/up.gif" alt="Up"></a></td><td width="40%" align="right"> <a accesskey="n" href="ch04s04.html"><img src="AllResources/IconsGIF/next.gif" alt="Next"></a></td></tr><tr><td width="40%" align="left" valign="top">4.2.
|
|---|
| 555 | Material
|
|---|
| 556 | </td><td width="20%" align="center"><a accesskey="h" href="index.html"><img src="AllResources/IconsGIF/home.gif" alt="Home"></a></td><td width="40%" align="right" valign="top"> 4.4.
|
|---|
| 557 | Hits
|
|---|
| 558 | </td></tr></table></div></body></html>
|
|---|
