Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Electromagnetism wikipedia , lookup
Field (physics) wikipedia , lookup
Introduction to gauge theory wikipedia , lookup
Thomas Young (scientist) wikipedia , lookup
Time in physics wikipedia , lookup
Aharonov–Bohm effect wikipedia , lookup
Casimir effect wikipedia , lookup
Matter wave wikipedia , lookup
Wave–particle duality wikipedia , lookup
RF resonant cavity thruster wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
LINACS Alessandra Lombardi and Jean-Baptiste Lallement CERN http://lombarda.home.cern.ch/lombarda/juasLINAC/ 1 Contents • Lesson 1 : introduction, RF cavity • Lesson 2 : from RF cavity to accelerator • Lesson3 : single particle dynamics in a linear accelerator • Lesson 4 : multi-particle dynamics in a linear accelerator and –time permittingbeam dynamics tour of linac2 • Guided study : Drift Tube Linac Design • Visit around PS : linac2 and linac3 ?? 2 credits • much of the material is taken directly from Thomas Wangler USPAS course (http://uspas.fnal.gov/materials/SNS_Front-End.ppt.pdf) and Mario Weiss and Pierre Lapostolle report (Formulae and procedures useful for the design of linear accelerators, from CERN doc server) • from previous linac courses at CAS and JUAS by Erk Jensen, Nicolas Pichoff, Andrea Pisent,Maurizio Vretenar , (http://cas.web.cern.ch/cas) 3 LECTURE 1 • what is a LINAC • historical introduction • parameters of a Radio Frequency (RF) cavity 4 motivation • particle beams accelerated in controlled condition are the probe for studying/acting the structure of matter and of the nucleus • controlled condition means generating a high flux of particles at a precise energy and confined in a small volume in space 5 what is a linac • LINear ACcelerator : single pass device that increases the energy of a charged particle by means of an electric field • Motion equation of a charged particle in an electromagnetic field x positionvector d x q dx E B 2 dt m dt 2 q, m ch arg e, mass E , B electric , magneticfield t time 6 what is a linac-cont’ed 2 d x q dx E B 2 dt m dt type of particle : charge couples with the field, mass slows the type of structure acceleration 7 Rate of change of energy d x q dx E B 2 dt m dt 2 dp dx q E B dt dt can be written as : p momentum W energy dW dx dp dx dx q E B dt dt dt dt dt Energy change via the electric field 8 type of particles – 4 groups • Electrons : – – – – High energy collider High-quality e- beam for FEL; Medical/Industrial irradiation; Neutron sources • protons and light ions : – Synchrotron injectors : High intensity, high duty-cycle – Neutron sources : High Power. Material study, transmutation, nuclear fuel production, irradiation tools, exotic nucleus production • heavy ions – Nuclear physics research : High intensity, high duty-cycle – Implantation : Semi-conductors – Driver for inertial-confinement fusion • short lived particles (e.g. muons) 9 type of linacs electric field static time varying induction Radio Frequency Linac 10 static linac • device which provides a constant potential difference (and consequently electric field). Definition of the Volt, measure of the energy in eV. • acceleration is limited to few MeV. Limitation comes from electric field breakdown • still used in the very first stage of acceleration when ions are extracted from a source. 11 induction linac 12 Radio Frequency Linac • acceleration by time varying electromagnetic field overcomes the limitation of static acceleration • First experiment towards an RF linac : Wideroe linac 1928 • First realization of a linac : 1931 by Sloan and Lawrence at Berkeley laboratory 13 Wideroe linac potassium ionBUNCHED lenght of the tube proportional to the velocity 25 kV 1 MHz • the energy gained by the beam (50 keV) is twice the applied voltage (25 keV at 1 MHz) 14 from Wideroe to Alvarez linac • to proceed to higher energies it was necessary to increase by order of magnitude the frequency and to enclose the drift tubes in a cavity (resonator) • this concept was proposed and realized by Luis Alvarez at University of California in 1955 : A 200 MHz 12 m long Drift Tube Linac accelerated protons from 4 to 32 MeV. • the realization of the first linac was made possible by the availability of high-frequency power generators developed for radar application during World War II 15 principle of an RF linac RF power supply 1) RF power source: generator of electromagnetic wave of a specified frequency. It feeds a 2) Cavity : space enclosed in a metallic boundary which resonates with the frequency of the wave and tailors the field pattern to the 3) Beam : flux of particles that we Wave guide Power coupler push through the cavity when the field is maximized as to increase its 4) Energy. Cavity 16 A (Linac) RF System: transforms mains power into beam power RF line Mains 220 V DC Power supply RF Amplifiers Beam in W, i Cavity Beam out W+DW, i Transforms mains power into DC power Transforms DC power Transforms RF power into RF power into beam energy [klystron/tube efficiency] [efficiency=shunt impedance] 17 designing an RF LINAC • cavity design : 1) control the field pattern inside the cavity; 2) minimise the ohmic losses on the walls/maximise the stored energy. • beam dynamics design : 1) control the timing between the field and the particle, 2) insure that the beam is kept in the smallest possible volume during acceleration 18 electric field in a cavity • assume that the solution of the wave equation in a bounded medium can be written as E( x, y, z, t ) E ( x, y, z ) e function of space jt function of time oscillatin at freq = ω/2π • cavity design step 1 : concentrating the RF power from the generator in the area traversed by the beam in the most efficient way. i.e. tailor E(x,y,z) to our needs by choosing the appropriate cavity geometry. 19 cavity geometry and related parameters definition field y beam x Cavity L=cavity length z 1-Average electric field 2-Shunt impedance 3-Quality factor 4-Filling time 5-Transit time factor 6-Effective shunt impedance 20 standing vs. traveling wave Standing Wave cavity : cavity where the forward and backward traveling wave have positive interference at any point 21 cavity parameters-1 • Average electric field ( E0 measured in V/m) is the space average of the electric field along the direction of propagation of the beam in a given moment in time E( x, y, z, t ) E ( x, y, z ) e jt when F(t) is maximum. L 1 E0 Ez ( x 0, y 0, z )dz L0 • physically it gives a measure how much field is available for acceleration • it depends on the cavity shape, on the resonating mode and on the frequency 22 cavity parameters-2 • Shunt impedance ( Z measured in Ω/m) is defined as the ratio of the average electric field squared (E0 ) to the power (P) per unit length (L) dissipated on the wall surface. Z • • • E 2 0 L P or Z 2 0 E dL for TW dP Physically it is a measure of well we concentrate the RF power in the useful region . NOTICE that it is independent of the field level and cavity length, it depends on the cavity mode and geometry. beware definition of shunt impedance !!! some people use a factor 2 at the denominator ; some (other) people use a definition dependent on the cavity length. 23 cavity parameters-2 optimized (from the ZTT point of view) cavity offers minimum surface for the max volume : spherical cavity. y x z 24 cavity parameters-2 But a more realistic shape includes –at least- an iris for the beam to pass through! y x z 25 cavity parameters-3 • Quality factor ( Q dimension-less) is defined as the ratio between the stored energy (U) and the power lost on the wall (P) in one RF cycle (f=frequency) 2 f Q U P • Q is a function of the geometry and of the surface resistance of the material : superconducting (niobium) : Q= 1010 normal conducting (copper) : Q=104 example at 700MHz 26 cavity parameters-3 • SUPERCONDUCTING Q depends on temperature : – 8*109 for 350 MHz at 4.5K – 2*1010 for 700 MHz at 2K. • NORMAL CONDUCTING Q depends on the mode : – 104 for a TM mode (Linac2=40000) – 103 for a TE mode (RFQ2=8000). 27 cavity parameters-4 • filling time ( τ measured in sec) has different definition on the case of traveling or standing wave. • TW : the time needed for the electromagnetic energy to fill the cavity of length L L dz tF v z 0 g velocity at which the energy propagates through the cavity • SW : the time it takes for the field to decrease by 1/e after the cavity has been filled tF 2Q measure of how fast the stored energy is dissipated on the 28 wall cavity parameters-5 • transit time factor ( T, dimensionless) is defined as the maximum energy gain per charge of a particles traversing a cavity over the average voltage of the cavity. • Write the field as Ez( x, y, z, t ) Ez ( x, y, z )e i (t ) • The energy gain of a particle entering the cavity on axis at phase φ is L • DW qEz (o, o, z )e i (t ) dz 0 29 cavity parameters-5 • assume constant velocity through the cavity (APPROXIMATION!!) we can relate position and time via z v t ct • we can write the energy gain as DW qE0 LT cos • and define transit time factor as L E z e j z c z T 0 L E z dz z 0 dz T depends on the particle velocity and on the gap length. IT DOESN”T depend on the field 30 cavity parameters-5 • NB : Transit time factor depends on x,y (the distance from the axis in cylindrical symmetry). By default it is meant the transit ime factor on axis • Exercise!!! If Ez= E0 then L L=gap lenght β=relativistic parametre λ=RF wavelenght sin T L 31 cavity parameter-6 ttf for 100 keV protons, 200 MHz., parabolic distribution 1 0.8 0.6 0.4 0.2 0 0 2 4 6 8 10 12 -0.2 lfield (cm) if we don’t get the length right we can end up decelerating!!! 32 effective shunt impedance • It is more practical, for accelerator designers to define cavity parameters taking into account the effect on the beam • Effective shunt impedance ZTT Z E 2 0 L P measure if the structure design is optimized E T ZTT 2 0 L P measure if the structure is optimized and adapted to the velocity of the particle to be accelerated 33 limit to the field in a cavity • normal conducting : – heating – Electric peak field on the cavity surface (sparking) • super conducting : – quenching – Magnetic peak field on the surface (in Niobium max 200mT) 34 Kilpatrick sparking criterion (in the frequency dependent formula) f = 1.64 E2 exp (-8.5/E) Kilpatrick field 40 electric field [MV/m] 35 30 25 20 15 10 5 0 0 100 200 300 400 500 600 700 800 900 1000 frequency [MHz] GUIDELINE nowadays : peak surface field up to 2*kilpatrick field Quality factor for normal conducting cavity is Epeak/EoT 35 summary of lesson 1 • first step to accelerating is to fill a cavity with electromagnetic energy to build a resonant field. in order to be most efficient one should : 1) concentrate the field in the beam area 2) minimise the losses of RF power 3) control the limiting factors to putting energy into the cavity • This is achieved by shaping the cavity in the appropriate way 36 Photo gallery • 352 MHz cavities for 3 MeV protons • 80 MHz cavity for muons 37 352 MHz cavity 38 88 MHz test cavity (made from an 114 MHz structure) 88 MHz cavity 2 MW amplifier Nose Cone (closed gap) 39 LECTURE 2 • modes in a resonant cavity • TM vs TE modes • types of structures • from a cavity to an accelerator 40 wave equation -recap • Maxwell equation for E and B field: 2 2 2 1 2 2 2 2 2 2 E 0 x y z c t • • 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 : E// 0 B 0 41 TE or TM modes • TE (=transverse electric) : the electric field is perpendicular to the direction of propagation. in a cylindrical cavity n : azimuthal, TE nml m : radial l longitudinal component • TM (=transverse magnetic) : the magnetic field is perpendicular to the direction of propagation n : azimuthal, TM nml m : radial l longitudinal component 42 wave equation-recap • • in cylindrical coordinates the solution for a TM wave can be expressed as Ez ARr e j t k z z The function () is a trigonometric function with m azimuthal periods the function R(r), is given with the Bessel function of first kind, of order m and argument sqrt (2/c2-kz2)r: 1 d 2 m2 0 2 d d 2 R 1 dR 2 m2 2 k R 0 z dr 2 r dr c 2 r2 2 2 AJ K r Rr AJ m k r z m r c2 • ,At the boundary (a cylinder of radius a), the condition for TM waves is Ez = 0, i. e. Jm(Krr) = 0 , and the first solution (lowest frequency) is for the TM 01 wave, with Kra = 2.405 or Kr = 2.405/a • dispersion relation links, for a given wave type and mode, the frequency of oscillation to the phase advance per unit length k 2 c2 K r2 k z2 fixed by boundary conditions 43 dispersion diagram Backward wave Forward wave Kz>0 cut off frequency 44 wave equation- recap • consider one component of the wave equation and express the solution as a product of functions like (travelling wave case) Ez AR(r )( )e j t k z z z v ph t kz being the angular frequency and kz the phase advance per unit length; • the phase velocity must be matched to the velocity of the particle that needs to be accelerated. In empty cavities Vph c so the waves must be slowed down by loading the cavity with periodic obstacles. disc loaded cavity. The obstacles delimit cells, and each cell is a resonator, coupled to its neighbours through the central aperture 45 phase velocity /group velocity Ez AR(r )( )e j t k z z moving with the wave one can put (t - kz z) = 0 z v ph t kz velocity of the wave phenomenon > c to satisfy boundary condition the electromagnetic energy propagates with the a smaller velocity, the group velocity, given by : d vg dk z 46 wave equation-recap • • in a periodic structure of period l the solution of the wave equation is such that --- for a given frequency and mode of oscillation, and in absence of losses, the solution may differ from a period to the next only by a factor like jk z l (Floquet theorem) e • --- the complicated boundary conditions can be satisfied only by a whole spectrum of modes called space harmonics. E r , z e j t k z z an r e j 2n / l z n • d 2 an r 1 dan r K rnan r 0 2 r dr dr 2n K kz c l 2 2 2 rn For each n one has a travelling wave with its own, slowed down velocity vph. The an are modified Bessel functions: an(r) = An I0(krr) dispersion relation for a chain of coupled oscillators 47 wave equation-recap • • • • • • for a given wave type and mode, there is a limited passband between o and ; at these points, vg = 0; the bigger the coupling between cells, the bigger the passband; for a given frequency, there is an infinite series of space harmonics, with the same vg, but with different vph; when the electromagnetic energy propagates only in one direction (solid curves on the diagram) travelling wave accelerator, TW; when the energy is reflected back and forth at both ends of the cavity (solid and dotted curves) standing wave accelerator, SW; if vph and vg in the same direction forward wave; if in opposite directions backward wave; travelling wave accelerators operate near the middle of the passband, where vg is maximum and the mode spacing biggest, see point A standing wave accelerators operate on the lower or upper end of the passband, point B or C , because only there the direct and reflected wave have the same vph, and they both accelerate particles. At these points the group velocity is zero. 48 TE modes dipole mode quadrupole mode used in Radio Frequency Quadrupole 49 TM modes TM010 mode , most commonly used accelerating mode 50 cavity modes • • 0-mode Zero-degree phase shift from cell to cell, so fields adjacent cells are in phase. Best example is DTL. • • π-mode 180-degree phase shift from cell to cell, so fields in adjacent cells are out of phase. Best example is multicell superconducting cavities. • • π/2 mode 90-degree phase shift from cell to cell. In practice these are biperiodic structures with two kinds of cells, accelerating cavities and coupling cavities. The CCL operates in a π/2structure mode. This is the preferred mode for very long multicell cavities, because of very good field stability. 51 basic accelerating structures • Radio Frequency Quadrupole • Interdigital-H structure • Drift Tube Linac • Cell Coupled Linac • Side Coupled Linac 52 derived/mixed structure • RFQ-DTL • SC-DTL • CH structure 53 Radio Frequency Quadrupole 54 Radio Frequency Quadrupole 55 Radio Frequency Quadrupole cavity loaded with 4 electrodes TE210 mode 56 RFQ Structures 57 four vane-structure 1. capacitance between vanetips, inductance in the intervane space 2. each vane is a resonator 3. frequency depends on cylinder dimensions (good at freq. of the order of 200MHz, at lower frequency the diameter of the tank becomes too big) 4. vane tip are machined by a computer controlled milling machine. 5. need stabilization (problem of mixing with dipole modeTE110) 58 four rod-structure • capacitance between rods, inductance with holding bars • each cell is a resonator • cavity dimensions are independent from the frequency, • easy to machine (lathe) • problems with end cells, less efficient than 4vane due to strong current in the holding bars59 transverse field in an RFQ + - alternating gradient focussing structure with period length (in half RF period the particles have travelled a length /2 ) + - - + + - 60 transverse field in an RFQ DT1 DT3 t0 t1 DT2 t2 DT5 t3 DT4 t4 time RF signal - ion beam + - + - + animation!!!!! - + electrodes DT1,DT3...... t0,t1,t2........ .... DT2,DT4..... 61 acceleration in RFQ longitudinal modulation on the electrodes creates a longitudinal component in the TE mode 62 acceleration in an RFQ D (1 ) 2 2 longitudinal radius of curvature modulation X aperture aperture beam axis 63 important parameters of the RFQ q V 1 1 I o ka I o mka B 2 2 m0 a f a m I o ka I o mka type of particle limited by sparking Transverse field distortion due to modulation (=1 for un-modulated electrodes) m 1 2 E0T 2 V m I o (ka) I o (mka) 4 2 Accelerating efficiency : fraction of the field deviated in the longitudinal direction (=0 for un-modulated electrodes) cell length transit time factor 64 .....and their relation 2 I o ka I o mka m 1 I 0 (ka) 1 2 2 m I ka I mka m I (ka) I (mka) o o o o focusing efficiency accelerating efficiency 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 65 RFQ • • • • • • The resonating mode of the cavity is a focusing mode Alternating the voltage on the electrodes produces an alternating focusing channel A longitudinal modulation of the electrodes produces a field in the direction of propagation of the beam which bunches and accelerates the beam Both the focusing as well as the bunching and acceleration are performed by the RF field The RFQ is the only linear accelerator that can accept a low energy CONTINOUS beam of particles 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)) 66 Interdigital H structure 67 Interdigital H structure the mode is the TE110 68 Interdigital H structure •stem on alternating side of the drift tube force a longitudinal field between the drift tubes •focalisation is provided by quadrupole triplets places OUTSIDE the drift tubes or OUTSIDE the tank 69 IH use • very good shunt impedance in the low beta region (( 0.02 to 0.08 ) and low frequency (up to 200MHz) • not for high intensity beam due to long focusing period • ideal for low beta heavy ion acceleration 70 Drift Tube Linac 71 DTL – drift tubes Quadrupole lens Drift tube Tuning plunger Post coupler Cavity shell 72 Drift Tube Linac 73 DTL : electric field Mode is TM010 DTL The DTL operates in 0 mode for protons and heavy ions in the range =0.04-0.5 (750 keV - 150 MeV) 1.5 E 1.5 1 1 0.5 0.5 0 Synchronism condition (0 mode): 0 0 20 40 60 0 -0.5 -0.5 -1 -1 -1.5 -1.5 80 20 100 40 120 60 140 80 l= 100 120 z 140 l c f The beam is inside the “drift tubes” when the electric field is decelerating The fields of the 0-mode are such that if we eliminate the walls between cells the fields are not affected, but we have less RF currents and higher shunt impedance 75 Drift Tube Linac 1. There is space to insert quadrupoles in the drift tubes to provide the strong transverse focusing needed at low energy or high intensity 2. The cell length () can increase to account for the increase in beta the DTL is the ideal structure for the low - low W range 76 RFQ vs. DTL DTL can't accept low velocity particles, there is a minimum injection energy in a DTL due to mechanical constraints 77 Side Coupled Linac Chain of cells, coupled via slots and off-axis coupling cells. Invented at Los Alamos in the 60’s. Operates in the /2 mode (stability). CERN SCL design: Each klystron feeds 5 tanks of 11 accelerating cells each, connected by 3-cell bridge couplers. Quadrupoles are placed between tanks. The Side Coupled Linac multi-cell Standing Wave structure in /2 mode frequency 800 - 3000 MHz for protons (=0.5 - 1) Rationale: high beta cells are longer advantage for high frequencies • at high f, high power (> 1 MW) klystrons available long chains (many cells) • long chains high sensitivity to perturbations operation in /2 mode Side Coupled Structure: - from the wave point of view, /2 mode - from the beam point of view, mode 79 Room Temperature SW structure: The LEP1 cavity 5-cell Standing Wave structure in mode frequency 352 MHz for electrons (=1) To increase shunt impedance : 1. “noses” concentrate E-field in “gaps” 2. curved walls reduce the path for RF currents “noses” BUT: to close the hole between cells would “flatten” the dispersion curve introduce coupling slots to provide magnetic coupling 80 example of a mixed structure : the cell coupled drift tube linac linac with a reasonable shunt impedance in the range of 0.2 < < 0.5, i. e. at energies which are between an optimum use of a DTL and an SCL 81 accelerator example of a mixed structure : the cavity coupled drift tube linac Single Accelerating CCDTL tank 1 Power coupler / klystron ABP group seminar 16 march 06 Module CCDTL – cont’ed • In the energy range 40-90 MeV the velocity of the particle is high enough to allow long drifts between focusing elements so that… • …we can put the quadrupoles lenses outside the drift tubes with some advantage for the shunt impedance but with great advantage for the installation and the alignment of the quadrupoles… • the final structure becomes easier to build and hence cheaper than a DTL. • The resonating mode is the p/2 which is intrinsically stable 83 Coupling cell 1st Half-tank (accelerating) 2nd Half-tank (accelerating) ABP group seminar 16 march 06 overview Ideal range of frequency beta Particles RFQ Low!!! - 0.05 40-400 MHz Ions / protons IH 0.02 to 0.08 40-100 MHz Ions and also protons DTL 0.04-0.5 100-400 MHz Ions / protons SCL Ideal Beta=1 But as low as beta 0.5 800 - 3000 MHz protons / electrons take with CAUTION! 85 Summary of lesson 2 • wave equation in a cavity • loaded cavity • TM and TE mode • some example of accelerating structures ad their range of use 86