The Touschek Module
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The Touschek Module in MAD-X. Catia Milardi (LNF-INFN) Frank Zimmermann (CERN) Frank Schmidt (CERN). Topics. Theoretical approach User instructions Differences with MAD-8 Examples Limitations Further developments. Generalities.

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The Touschek Module in MAD-X

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The touschek module in mad x

The Touschek Module

in MAD-X

Catia Milardi (LNF-INFN)

Frank Zimmermann (CERN)

Frank Schmidt (CERN)


The touschek module in mad x

Topics

  • Theoretical approach

  • User instructions

  • Differences with MAD-8

  • Examples

  • Limitations

  • Further developments


The touschek module in mad x

Generalities

  • Particles in a relativistic bunch undergo Coulomb scattering involving:

    • multiple hits leading to increase of all beam sizes (IBS)

    • two particles transforming a small transverse momentum in to a large longitudinal one with consequent loss of both particles (Touschek effect).

  • The Touschek effect depends on beam energy and on the bunch volume so it is much more concerning for:

    • low-energy machines

    • small emmittance machine

    • high bunch current


The touschek module in mad x

Piwinski’s approach

Piwinski, TheTouschek effect in strong focusing storage ring, Desy 98-179, Nov. 1998.

The particle loss rate 1/T due to the Touschek effect is computed:

  • considering two arbitrary particles in their center of mass system

  • writing the Møller scattering cross section taking into account:

    - two-dimensional distribution of transverse momenta (due to both betatron and synchrotron oscillation)

    - beam envelopes variation

    - gaussian distribution in all beam coordinates


The touschek module in mad x

Particle loss rate due to the

Touschek effect

• rp classical particle radius

• Np number of particles per bunch

• g particle energy in rest mass unit

• ssbunch length

• sx,z standard deviation of the beam transverse size

• sp relativemomentum spread

• Dx,z dispersion function


The touschek module in mad x

Piwinski’s integral

I0 is the 0th order Bessel function


The touschek module in mad x

… in order to simplify numerical integration


The touschek module in mad x

RF momentum acceptance

computed from the bucket size taking into account the energy loss per turn due to synchrotron radiation U0

V0RF voltage

fsRF synch phase

h harmonic number

q overvoltage factor

h

If U0 = 0


The touschek module in mad x

Momentum acceptance

in presence of several RF systems

  • The Touschek module can handle machines with more than one RF systems with different frequencies and/or voltages.

  • The momentum acceptance is computed assuming:

    • • The maximum phase on the separatrix is defined by the reference RF having the lowest frequency and voltage V ≠ 0.

    • • All systems are synchronized with the reference RF.

  • Different RF arrangements are not supported and would require a modification of the module !!


  • The touschek module in mad x

    Energy loss per turn due to SR

    is computed from I2returned by theTWISS_summtable when the TWISS chrom option is invoked

    • U0 = 0 when I2 is:

      • vanishing,undefined or not computed


    The touschek module in mad x

    About ss and sp

    The BEAM command computes the synchrotron tune qsfrom the RF cavity parameters.

    Then ssand sp for leptonscome from:

    Et longitudinal emittance

    L machine circumference

    Defining Et < 0 in the BEAM command allows the user to assign the ssand sp values


    The touschek module in mad x

    For a generic element in the DAFNE lattice

    Using a more accurate routine (CJYDBB) for I0 calculation produces negligible differences in the evaluation of the Piwinski G function, but removing the discontinuity results in a reduction by a factor 2 in the overall execution time.


    The touschek module in mad x

    Touschek lifetime evaluation in MAD-8

    • T is computed when the BMPM TOUSCH option is invoked.

    • The BMPM module could not handle:

      • combined function dipoles

      • machine elements with TILT ≠ 0

    • It was based on some simplifying assumptions about:

      • beam emittance

      • damping partition numbers

    • Computation formalism see Gygi, Keil, Jowett, BeamParam, CERN/LEP-TH/88-2


    The touschek module in mad x

    Input Instructions

    ………

    RFCAV: rfcavity, l = lcav, volt = 0.09, lag = 0.49, harmon = 120,

    tfill = 1., shunt = 0.2, pg = 0.1;

    RESBEAM;

    BEAM, PARTICLE = positron, energy = .51,sequence = wholekf ,

    npart = 2.E+10, ex = .4E-6 , ey = 1.1964E-9 ,

    et = -6.E-6 , sige = .0003, sigT = .02, radiate = true;

    ………

    use, period = wholekf;

    twiss, chrom, sequence = wholekf, centre, table, file =wholekf0.txt, save;

    touschek, tolerance = 1.e-07, file = name;

    STOP;

    http://mad.home.cern.ch/mad/touschek/touschek.html


    The touschek module in mad x

    Output File

    • name beamline element

    • s azimuth of the element center

    • tli elementcontribution to 1/T

    • tliw tli*Le/L Le element length, L ring circumference

    • tlitot sum of loss rates tliw through the beamline elements

    • The Touschek lifetime T is:

      • T = 1/tlitot @ the end of the beamline


    The touschek module in mad x

    Contributions tliw to the Loss Rate

    from the elements of the DAFNE lattice


    The touschek module in mad x

    Touschek lifetime, emittances etc. vs. RF voltage

    for CLIC (DR)

    beam parameters were computed

    by Maxim and include IBS effect


    The touschek module in mad x

    Touschek lifetime evaluation

    http://frs.home.cern.ch/frs/mad-X_examples/touschek/


    The touschek module in mad x

    • DAFNE experiences limitations of the transverse aperture due to the presence of:

      • COLLIMATORS affecting physical aperture

      • WIGGLERS and SEXTUPOLES having non-linear terms affecting dynamic aperture

    • As a consequence the maximum stable relative momentum deviation evaluated from RF acceptance is larger than the real one leading to an optimistic evaluation of the Touschek lifetime by a factor ≈2.


    The touschek module in mad x

    Further developments

    • Introduce the dynamic momentum Acceptance Ap

    • in the evaluation of the Touschek Lifetime (if smaller than RF acceptance)

      • Since Ap depends on:

        • geometrical aperture

        • tune shift on amplitude from non linear terms

        • tune proximity to resonances

      • it can be evaluated by tracking processes only and then passed as an input parameter to the Touschek module.

    • Introduce the exact evaluation of the equilibrium energy spread, in order to take into account rings with SRFF

    • Add Uo to the input parameters in order to deal with high order modes


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