BEAM SIMULATION OF THE MAIN LINAC OF THE ILC

BEAM SIMULATION OF THE MAIN LINAC OF THE ILC MCDAVIS FASUGBA LINCOLN UNIVERSITY OF PENNSYLVANIA PAUL LEBRUN FERMILAB AUGUST 8, 2006

CONTENTS • What is the ILC? • Overview of FERMILAB and the ILC • Main linac parameters • Simulation of the main linac • Simulating the particle propagation • Analysis and Results • Conclusion • Acknowledgement

Need for an ILC • New physics is expected at the TeV Scale • ILC has well defined energy which can be varied • Discoveries at LHC will lead to questions such as • Is “neutralino” dark matter • How many extra dimensions are there? • Can we see super-symmetry? • All these questions may not be answered at the LHC, and as such we need a new collider.

FERMILAB and the ILC • Fermilab is home to the world’s highest energy particle accelerator. • FERMILAB may also house the ILC • The ILC will be purely an international effort • It is believed to answer some compelling questions together with the LHC • FERMILAB is an active participant in this project

MAIN LINAC PARAMETERS • ~20 km in length • Injected bunch Charge: 2x10e10(Particles/bunch) • Injection energy: 15 GeV • Final energy: 250 GeV • Acceleration gradient: ~30MV/m • Beam Parameters • Momentum spread: ~1% at injection • Bunch length:300μm • Transverse emittance: 400x20 μm.mrad (these are emittances more than 50 times smaller than what we are used to in the tevatron complex)

Need for Simulation • Understand and solve low emittance transport problem • If built with a realistic practical mechanical tolerance, emittance will be many order of magnitude above what we need for a high luminosity collider. • First step is to understand how a single particle behaves down the linac when it is “offset” transversely.

SINGLE PARTICLE SIMULATION IN THE MAIN LINAC • Study the trajectory of the particle along the Linac • Record the position of the particle at each BPM • Making plots to understand the physics behind the behavior of the beam, changing particle position in 6-d phase space.

TERMS AND THEIR MEANINGS • Emittance : The extent occupied by a beam as travels in an accelerator. • Phase space: space in which states of a system are represented. • Phase space usually contains all possible values of position and momentum variables • Bunch: collection of particles moving towards a target • BPM (beam position monitor): This is a device to detect and record the position of beam bunches moving through a segment of the accelerator

SIMULATING THE PARTICLE PROPAGATION • Writing set of codes for the simulation • Extracting the data • Analyzing the data and making simple plots

CHEF SOFTWARE • It is a large framework to simulate accelerator systems and beam lines. • Written by Leo Michelotti et al • Written in C++ • Used to simulate the Fermilab booster and Tevatron • Recently certified for low emittance transport in positron Linacs. • It comes with examples which I used and modified

Codes written serves various purposes. 1. Simulate the Propulsion of the particle from one end of the linac to the other. Ensuring the beam is not disrupted by kicks given by the cavities. Ensuring it maintains a physical aperture restriction. Beam must be confined within the beam pipe. Written Codes

Brief sections of program written A section of the codes written looks like this: for (int i=0; i<1; i++){ // Example 2 loop cerr<<"i=" << i<< endl; Particle* prtEx2 = new Positron( bmlPtr->Energy() ); prtEx2->set_x ( myOptions.x ); double newPInit =-1e-3+i*1e-3; prtEx2->set_y ( myOptions.y ); prtEx2->set_cdt( myOptions.cdt ); prtEx2->set_npx( myOptions.px ); prtEx2->set_npy( myOptions.py ); prtEx2->set_ndp(newPInit ); cout << " Ready to propagate " << endl; BeamlineIterator biCK( bmlPtr ); double s = 0.; int numLinesPrinted= 0; int step=0; double minDistanceBetweenPrints = 10.; // in meter double sAtPreviousPrint = -20.; The code on the left defines a positron,and propagates it down a linac with a certain Initial offset. All initial conditions are set in the data structure “myOptions”

Section of BPM analysis code ofstream out("values1.txt"); dout<<"BPM"<<setw(20)<<" dpp"<<endl; BeamlineIterator biCK( bmlPtr ); cout << " got biCK Late Friday " << endl; double s = 0.; while(( q = biCK++ )) { q->propagate( *prtEx2 ); s += q->Length(); if(0==strcmp("monitor",q->Type() ) ){ double yNow = prtEx2->get_y(); double xNow = prtEx2->get_x(); double pNow = prtEx2->get_ndp(); double R = std::sqrt((xNow*xNow)+(yNow*yNow));//radius of the orbit BPM++; if(R>0.003){ dout<<BPM<<setw(20)<<pNow<<endl; break; } } // end of BPM analysis code } out<<BPM<<setw(20)<<prtEx2->get_ndp()<<endl; cerr<<"i=" << i<< endl; biCK.reset(); // Not really necessary here, but what the heck. delete prtEx2; } out.close(); bmlPtr->eliminate(); exit(2); return 0; This helps set the physical aperture restriction and aborts propagation if exceeded Offset=5μm at injection

Results and Analysis • Plot of vertical-offset against distance • Quadrupole strength increased Trajectory disrupted due to high kicks from quadrupoles

Dampening of Betatron Oscillations S(m) The Plot of vertical offset against distance For a fixed matched lattice, the Amplitude of the oscillations Reduces down the linac y(m))

Physical/Dynamic aperture restriction Plot of BPM against(δp/p) The graph at the left Indicates when the aperture restriction is exceeded. δp/p =(p-p0)/p0

Conclusion • The simulation has helped in understanding certain behavior of the beam. • It throws more light on some key aspects of the beam dynamics in a Linac • It provides solution to some low emittance transport problems

Acknowledgement • I thank God for giving me this summer opportunity • I thank Dianne and Elliott for making it possible for me to be here at FERMILAB • I also thank Paul for his support he gave me as my supervisor. • For all the other SISTers, it was another fun filled summer.

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BEAM SIMULATION OF THE MAIN LINAC OF THE ILC