Radio Frequency Quadrupole

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Radio Frequency Quadrupole. Alessandra Lombardi. RFQ CAS 2005 , Zeegse, 26 may 2005. Radio Frequency Quadrupole is on the school poster!. CERN RFQ1 520 keV protons. Contents. Motivation and historical introduction What is a radio frequency quadrupole (RFQ) ? Designing a RFQ - PowerPoint PPT Presentation

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  • Radio Frequency QuadrupoleAlessandra LombardiRFQ CAS 2005 , Zeegse, 26 may 2005

  • Radio Frequency Quadrupole is on the school poster!CERN RFQ1520 keV protons

  • ContentsMotivation and historical introduction

    What is a radio frequency quadrupole (RFQ) ?

    Designing a RFQ

    Frequently asked questions

  • RFQ history 1970 Kapchinskij and Teplyakov propose the idea of the radiofrequency quadrupole ( I. M. Kapchinskii and V. A. Teplvakov, Prib.Tekh. Eksp. No. 2, 19 (1970)).1974 experimental test of K&T idea at USSR Institute for High Energy Physics in Protvino. A 148.5-MHz RFQ accelerated 100-KeV protons to 620 KeV with an efficiency of 50%.1977 RFQ concept is published in the western world. Strong interest in Los Alamos National Laboratory (USA). Decision to test the RFQ principle for possible application in development of high-current low-emittance beams. Developments of computer codes for rfq design.1979 Start of P.O.P. (Proof-of-principle experiment) at Los Alamos . 425 MHz RFQ accelerates a 100-keV proton beam to 640 keV with an efficiency of 90%, as predicted by the codes. (14 Feb. 1980 ) Nowadays hundreds of RFQ accelerator are operating in the world

  • RFQ represented the missing link to high power beamHigh current and small emittance (powerful source)High energy (powerful and efficient accelerators)POWERFUL SOURCE :

    200 mA proton beam Emittance 1 pi mm mrad

    POWERFUL ACCELERATOR

  • Link between source and efficient accelerator The Radio Frequency Quadrupole is a linear accelerator which focuses bunches accelerates a continuos beam of charged particles with high efficiency and preserving the emittance

    Both the focusing as well as the bunching and acceleration are performed by the RF field

  • wave equation -recapMaxwell equation for E and B field:

    In free space the electromagnetic fields are of the transverse electro magnetic,TEM, type: the electric and magnetic field vectors are to each other and to the direction of propagation. In a bounded medium (cavity) the solution of the equation must satisfy the boundary conditions :

  • TE or TM modesTE (=transverse electric) : the electric field is perpendicular to the direction of propagation. in a cylindrical cavity

    TM (=transverse magnetic) : the magnetic field is perpendicular to the direction of propagationn : azimuthal, m : radial l longitudinal component n : azimuthal, m : radial l longitudinal component

  • TE modesdipole mode quadrupole mode used in Radio Frequency Quadrupole

  • Radio Frequency Quadrupole

  • Radio Frequency Quadrupolecavity loaded with 4 electrodes TE210 mode

  • RFQ Structuresfour-vane

    four-rod

    others (split coaxial,double H )

  • four vane-structurecapacitance between vanetips, inductance in the intervane space

    each vane is a resonator

    frequency depends on cylinder dimensions (good at freq. of the order of 200MHz, at lower frequency the diameter of the tank becomes too big)

    vane tip are machined by a computer controlled milling machine.

    need stabilization (problem of mixing with dipole modeTE110)

  • four rod-structurecapacitance between rods, inductance with holding barseach cell is a resonatorcavity dimensions are independent from the frequency, easy to machine (lathe)problems with end cells, less efficient than 4-vane due to strong current in the holding bars

  • transverse field in an RFQalternating gradient focussing structure with period length (in half RF period the particles have travelled a length /2 )

  • transverse field in an RFQanimation!!!!!

  • acceleration in RFQlongitudinal modulation on the electrodes creates a longitudinal component in the TE mode

  • acceleration in an RFQaperturemodulation X aperture

  • important parameters of the RFQAccelerating efficiency : fraction of the field deviated in the longitudinal direction(=0 for un-modulated electrodes)transit time factor cell lengthTransverse field distortion due to modulation (=1 for un-modulated electrodes)type of particlelimited by sparking

  • .....and their relation a=bore radius, ,=relativistic parameters, c=speed of light, f= rf frequency, I0,1=zero,first order Bessel function, k=wave number, =wavelength, m=electrode modulation, m0=rest q=charge, r= average transverse beam dimension, r0=average bore, V=vane voltage focusing efficiencyaccelerating efficiency

  • Beam dynamics design (very first approach) The beam dynamics in an RFQ determined by the geometrical parameter of the electrode structure

    Aperture : determines the focusing strenght and the acceptance.Depth of the modulation : determines the field availible for acceleration Distance between the peaks and the trough of the modulation determines the synchronicity between the field and the particles

  • Electrode structure aperturemodulation X aperture

  • Transverse plane-focusing quadrupole focusing (1) RF defocusing ( modulation ) (2) space charge defocusing (3) Z0 is the free-space impedance (376.73 Ohm), I is the beam current, f(p) is a geometrical factor p is the ratio of the transvese beam dimensions, r is the average transverse beam dimension, b the longitudinal . (1) (2) (3)

  • Longitudinal plane-bunchingSmootly change the velocity profile of the beam without changing its average energy

  • Longitudinal plane-acceleration use the rising part of the RF : receive less acceleration, late particles more (PHASE FOCUSING)

    late part.

    early part.

    synchr. part.

  • RFQ sections

    Radial matching to adapt the beam to a time-varying focusing system

    aperture smoothly brought to the average value

    shaping to give the beam a longitudinal structure

    Taper phase

    to 80,60 deg

    start modulation

    aperture such that focusing is constant

    bunching to bunch and begin acceleration

    Taper phase

    to 30,-20 deg

    modulation to max

    aperture such that focusing is constant

    acceleration to bring the beam to the final energy.

    Constant phase

    Constant modulation

    Constant aperture

    output matching to adapt the beam to the downstream users need.

  • High intensity vs. low intensityLOW INTENSITY RFQS CAN BE MADE SHORTER THAN THE CORRESPONDING HIGH INTENSITY ONES

    Emittance dominated

    Space charge dominated

    RMS

    over many cells w/o acceleration

    SHAPER

    shaping and acceleration

    fast bunching

    PRE-BUNCHER

    complete the bunching

    (almost no energy increase up to here)

    GENTLE BUNCHER

    bunching and acceleration

    fast transition to accelerating phase

    BOOSTER

    beam strongly bunched

    ((=-20,-15)

    ACCELERATOR

    beam bunched around (=-35,-30

    EXIT MATCHER

  • HIGH INTENSITY RFQ2 ( 200 mA protons)

  • LOW INTENSITY LEAD ION RFQ (100 A )

  • Why is the RFQ such a good focusing channel for low energy ions

  • RFQ vs. DTLDTL can't accept low velocity particles, there is a minimum injection energy in a DTL due to mechanical constraints

  • Why is the RFQ so efficient in bunching a beamDiscrete bunching

    Vs adiabatic bunching : movie

  • Why is the RFQ so efficient in bunching a beamDiscrete bunching

    Vs adiabatic bunching : movie

  • Why dont we accelerate to the final energy by using only RFQs ?CERN RFQ2Max accelerating efficiency is limited by geometry

    Chart5

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    A

    z (cm)

    Accelerating effciency

    Chart2

    0.250.62

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    11.05

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    21.83

    &A

    Page &P

    rfq2 working point

    ein=eout

    emitt out (I=0)

    emitt out (I=200mA)

    emittance i