geant4 applications to accelerator...

V. Daniel Elvira, FermilabG4 Users Meeting, February 21st , 2002

GEANT4 Applications to Accelerator Physics

V. Daniel [email protected]

February 21st 2002


• Accelerators

• G4 tools for beam physics (V. Daniel Elvira, P. Lebrun, P. Spentzouris, CPD/CD Fermilab)

• Applications

• Issues, Plans

Outline


Magnets: dipoles, quadrupoles, solenoidsBasic elements of an accelerator to bend, focus, capture a beam of particles.

B

VB⊗

1 2

B

Horizontal Vertical deflection

Uniform field provides focusing in the horizontal direction but a deflection in the direction of the field would make the particle spiral away


Weak Focusing

Cross section of a circular accelerator

B F=q V x B

rB

B 0y =

y

x

Focusing is weak because although there is also radial focusing, By gets weaker as a function of radius (gaps too large, and lots of iron !)

Particles above (below) midplane experience downward (upward) force vertical focusing


Strong FocusingAlternating gradient focusing (1952) by Livingston at BNL Cosmotron (magnets in a ring)

Quadrupole lens: focus horizontally and defocus vertically or vice-versa

Geometric optics: equal strength convex and concave lenses can produce net focusing (if their distance < focal length)

yB

xB

yy

BBx

xB

B xyxx

yy ∂

∂=

∂∂

∂∂

=∂

∂=


Solenoid Focusing

Large beam size (σx ~ σy ~1-10 cm), large angles

large aperture, thin lens approximation no longer valid: constx

xB

B yy ≠

∂∂

=

B

solenoid

B

Particle track

Bz=f(r,z), Br=g(r,z) Non-linear equations, horizontal and vertical motion not independent ( x-py & y-px correlations)

Characteristic feature of the Muon Collider/ Neutrino source design. Solenoids focus in two directions simultaneously.


The Solenoid Classclass Solenoid: public G4MagneticField {

int mynumptrxy, mynumptz;

double *mycoorrxy, *mycoorz;

double *mybrxy, *mybz;

vector<HepSpline1D> mysplz, mysplrxy;

vector<Sheet> sheetsInSol;

public:

Solenoid ( double minrxy, double maxrxy, int numptrxy, double minz, double maxz, int numptz, vector<Sheet> const &vsheets );

~Solenoid();

void GetFieldValue( const double Point[4], double *Bfield ) const;

}

251 cm

74 cm

Open Inventor

Defines a grid: r, z, Br , Bz

Spline fits of Bzand Br versus z for each r

Set of infinitely thin sheets of current

Linear interpolation of fits in r

Assembles the solenoid, builds grid and spline fits


class Sheet: public G4MagneticField {

int myid, mytype; float mythick, myrad, mylen, mycur; ThreeVector mylocation;

public:

Sheet ( ThreeVector location, int id, int type, float thick, float rad, float len, float cur ) :

mylocation(location), myid(id), mytype(type), mythick(thick), myrad(rad), mylen(len), mycur(cur)

{ ; }

void GetFieldValue ( const double Point[4], double *Bfield ) const;

virtual ~Sheet() { ; }

}; // Sheet

The Sheet Class

radius, length, and current

Analytic calculation of the magnetic field of the sheet


Global Field and Magnet SolidsIn the DetectorConstruction user class we construct:

• a global field result of an array of magnets

• a logical volume for each type of magnet

• physical volumes to place the array

AGlobalEMField* ff = new AGlobalEMField();

fieldMgr->SetDetectorField(ff);

LogSol = new SolenoidG4LogicVol (Solenoid *sol, G4Material *MatCoil,...);

SolenoidG4PhysVol(G4RotationMatrix *pRot, const G4ThreeVector &position,SolenoidG4LogicVol *SolLV, G4VPhysicalVolume *pMother, double fscale, AGlobalEMField *ff )

Pointer to global field

Set global field

Construct logical volume for each type of magnet

Place each magnet and add it to the global field


AccelerationResonant cavities provide both acceleration and focusing in the longitudinal direction

L

R

Pillbox cavityπ 2πφs

L: cavity length, R: cavity radius Vp : peak voltage ν: frequency φs: synchronous phaseVs: synchronous V

Vp

( )t?2p fsinrc

?2pJEt)(r,E s00z +

==

Vp

2.405Rc

?2p=

Ez = 0 at r = R (ν fixes radius)

L is fixed by Vz, ν, phase advance

Fast particles get a smaller kick than slow particles (longitudinal focusing)

Vs


E-E

nom

inal

(MeV

)

Longitudinal phase space distribution of a “bunch” of particles

Bucket Separatrix

c∆T

Wmax

( )s

nomimax

fp?p2

c3Tc?

EW

−≈

∝

The separatrix divides the regions of stable (inside the bucket) and unstable motion

Bucket size depends on the beam energy, and the r.f. frequency and synchronous phase

Example: Enominal=200 MeV

L=32 cm, R=57 cm Vp =16.5 MV/m ν=201.25 MHz φs= 25.7o

Wmax ~ 60 MeV CT∼80 cm


The EMPillbox Classclass EMPillBox: public G4ElectromagneticField {

double frequency; double length; double eMaxGradient; double delay; double phaseAccel; double rMaxCavity;

public:

EMPillBox (double freqIn, double length, double eMaxGradIn, double phaseAccIn, double delayIn);

void GetFieldValue(const double Point[4], double *Bfield ) const;

}; // class EMPillBox

time delay for a cavity to match synchronous phase

synchronous phase

Open Inventor

class RFCavityG4LogicVolclass LinacG4PhysVol

Logical volume, place a linac, and add it to global field

Beryllium windows

Copper walls

We can also construct magnets and r.f. cavities from given field maps, using the Classes:

EMrfmap & MagFieldmap


The BeamLiouville’s theorem: density in phase space of non interactive particles in a conservative system is invariant

Phase space volume enclosed by the separatrix or any given surface is conserved (shape may change), if acceleration is performed adiabatically

Normalized Longitudinal Emittance: εL= (σE σCT)/mc2

Normalized Transverse Emittance: εx= (σx σpx)/mc2

Lorenz invariant

Beta Function, β(s) is proportional to beam envelope (amplitud) along its path. It is determined by the accelerator lattice

Examples: β(s) = 2pc/eBz (solenoid) oscillating (FODO)


The ν SourceNeutrino beam based on µ storage ring (1.7 km long):• 16-24 GeV proton driver ( 1-1.5 MW)

• Carbon target: p π + κ

• Capture, decay into µ, bunching

• Muon cooling ( εx~1 cm, factor~10)

• Linac + recirculating linacs

• µ Storage ring ( 50 GeV), gives 1020 neutrinos/year

Challenges:• target facility• cooling channel


Muon Ionization Cooling

x x

z zP1

P2

θ1

θ2

θ1

θ2absorber

accelerator accelerator

absorberP3

θ1

+−= ⊥

Rµ3

trans

xx

LmEßß

fLe

dzde

Multiple scattering

Heating term (Mult.Scatt.)Cooling term +

lengthradiation:LBec2p

ß

dEdz

EßLv/cß

R

2trans

=

==

⊥

P2 < P1

All absorber classes inherit from the abstract class

AbsObj

Multiple Scattering is critical !


Example: Long Solenoid Channel

Cooling cell~2.5 m long

126 cm

All channel2nd flip

On axis On axis

220 m long (87 cooling cells), two field flip regions (3T to –3T & -7T to 7T)

P (GeV) vs Z (cm)

Electric field acceleration

Energy loss in material

No multiple scattering, straggling, or delta rays


Px versus x E versus CT( Final εx ~ 2 mm ) ( Final εL ~ 2 x Initial εL )

Published in proceedings of Particle Accelerator Conference, Chicago, June 2001 (Fermilab-Conf-01-182-T)


Example: Helical Channel

Other simulations:

Open Inventor

zxy

72 m long solenoidal + dipole field with wedge absorbers and thin cavities

0zTyx, BBzL2p

sincos,BB =

=

• Alternate Solenoid Channel (sFoFo), published in proceedings of PAC2001 and Feasibility Study II for a Neutrino Factory at BNL (2001)

• Bent Solenoid Channel, presented at Emittance Exchange Workshop, BNL 2000

• Low Frequency r.f. Cooling Channel, presented at International Cooling Experiment Workship, CERN 2001

• Cooling Experiment (MICE) Simulation (in progress)

Published in proc. of PAC 2001 (Fermilab-Conf-01-182-T)


GEANT3 to GEANT4 MigrationAll simulations previously shown were performed with a customized version of GEANT4.2.0. Double precision version of GEANT3 had been used previously. Migration started with GEANT4.1.0…………

• Ekin did not change when electric field present, and time dependent electricfields not supported

• Multiple scattering model changed. Default parameters would give results different from G3. Free parameter left to the user to set with SetScatteringParameter(value).

• Stochastic processes were not eliminated completely by turning off multiple scattering and using SetEnlossFluc(false); delta rays would still be produced

• We were confused by the meaning and use of the accuracy parameters: delta_cord, delta_interaction, delta_one_step_value

Twenty library files modified to produce the CPD/CD Fermilab version of GEANT4.2.0. We also had our own DataCards Class. Therefore………………

• update to newer G4 versions painful

• official release of G4 beam tools among ~10 users is a delicate matter


G4.4.0 (with Jan patch) IssuesNow G4 supports time dependent electric fields. It is time to interface the beam physics tools to G4.4.0.

No more customization of the GEANT4 library

(cm)

(GeV/c)

To do:

• Test time dependent electric field.

• Investigate accuracy & performance

• Study new multiple scattering model (5 parameters set by the user)

• Replace our DataCard Class by the use of Messenger Classes

• Manipulate multiple scattering and delta rays from Main() using messengers

It works!

Ez = f(z) & constant with time


Summary & PlansG3 to G4 migration & beam physics tools development has been successful

Useful studies performed, published in proposals, conference proceedings. A group of people ( < 10) are using the beam physics tools

But we are still using an un-officially patched version of G4.2.0

• Work closely with G4 collaboration until the long solenoid example works with an officially patched version of G4.4

• Release the example and the beam tools to the neutrino source (and the G4) collaborations

• Write documentation on the use of the tools

• Offer support to the users

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