Fundamental Concepts of Particle Accelerators Koji TAKATA KEK koji.takata@kek.jp http://research.kek.jp/people/takata/home.html Accelerator Course, Sokendai, Second Term, JFY2010 Oct. 28, 2010 The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Contents I I I I The Dawn of Particle Accelerator Technology I DC high voltage generators I Use of magnetic induction: betatron I Drift tube linac and cyclotron I Great progress just after world war II Basic Concepts I Principle of RF phase stability I Strong focusing I Synchrotron radiation (SR) I Collider I Technical issues Accelerators in Future I ERL (Energy Recovery Linac) : SR source of new type I LC : Linear Collider I µ-µ Collider and/or µ-Factory I Laser-plasma acceleration Livingston Chart Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II The Dawn of Particle Accelerator Technology I Artificial disintegration of atomic nuclei I First Accelerators I from DC Acceleration to RF Acceleration I Problems in RF Acceleration I Rapid Development of Electronics around World War II (1941 - 1945) or after Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II First artificial disintegration of atomic nuclei (1) I Ernest Rutherford’s discovery of nuclear disintegration (1917 - 1919) I He confirmed that protons were produced in a nitrogen-gas filled container in which a radioactive source emitting alpha particles was placed. α + 147 N → p + 168 O I This provoked strong demand for artificially generate high energy beams to study the nuclear disintegration phenomena in more detail. I Thus started the race for developing high energy accelerators, and Rutherford himself was a great advocator. Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II First artificial disintegration of atomic nuclei (2) I The first disintegration of atomic nuclei with accelerator beams was achieved at the Cavendish Laboratory in 1932 by John D. Cockcroft and Ernest T. S. Walton, who used 800 kV proton beams from a DC voltage-multiplier. p + 73 Li → α + α Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II DC HV Accelerators I I DC Generators:two major methods I Cockcroft & Walton’s 800 kV voltage-multiplier circuit with capacitors and rectifier tubes I Van de Graaff’s 1.5 MV belt-charged generator (1931) Electrostatic accelerators are still in use for the mass spectroscopy, because of their fine and stable tunability of the acceleration voltage. I analysis of the ratio archaeology 14 C/12 C : an important tool for Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II Cockcroft & Walton’s voltage-multiplier circuit V(3+cos ωt) V(1+cos ωt) V cos ωt V(5+cos ωt) AC 0 2V 4V 6V 0 Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II Cockcroft around 1932 See the picture in From X-rays to Quarks, page 227 by Segrè, E. (W. H. Freeman and Company, 1980) . Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II Glass Tube with Beam Acceleration Gaps Visit the home page : http://www.daviddarling.info/encyclopedia/C/Cockcroft.html Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II 750 keV Cockcroft-Walton Accelerator Used at KEK Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II Van de Graaff’s 1.5 MV Belt-charged Generator Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II Limitations in Electrostatic Accelerators I DC acceleration is limited by high-voltage breakdown (BD). I typical BD voltages for a 1cm gap of parallel metal plates Ambience air (1 atm) SF6 (1 atm) SF6 (7 atm) transformer oil UHV I Typical BD Voltages ≈ 30 kV ≈ 80 kV ≈ 360 kV ≈ 150 kV ≈ 220 kV no drastic increase in BD limits for much larger plate gaps. Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II High Voltage Breakdown of a Van de Graaff generator A demonstration of BD to housing walls. Search for the key word ”van der graaf generator” at http://en.wikipedia.org/wiki/ Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II Intermediate stage towards RF Acceleration Use of Faraday’s law of induction I Irrotational electric field due to magnetic flux change, a prelude to RF acceleration [Donald W. Kerst’s betatron (1940)]: ∇×E=− ∂B , ∂t then I Es ds = − C ∂ ∂t ∫∫ B · n dxdy = − S ∂ Φ ∂t Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II Kerst’s Betatron Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II Start of Real RF Accelerators Linear and/or Circular I Linear accelerator (linac) : I I I Gustaf Ising’s proposal (1925) Rolf Wideröe made a prototype of the Ising linac (1928) Multiple RF acceleration in a magnetic field I Ernest Lawrence’s cyclotron (1931): I the first circular accelerator repeated acceleration at the cyclotron frequency : ωc = eB⊥ /m Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II The first linac by Wideröe I I 25 kV per gap ×2 with the drift tube he convinced the scheme can be repeated indefinitely many times to reach higher beam energies RF Ion So urce Beam Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II First Cyclotrons See the picture in From X-rays to Quarks, page 229 by Segrè, E. (W. H. Freeman and Company, 1980) . A Riken cyclotron accelerated protons to 9 MeV and deuterons to 14 MeV (1939) Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II Circular Orbit of Charged Particles in Magnetic Field Search for the key word ”Cyclotron” in http://en.wikipedia.org/wiki/ Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II Principle of Cyclotron Operation RF Generator dee dee rn Magnetic Field rn+1(> rn) Electric Field beam dee dee Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II Problems in RF Acceleration I Linacs: I I Cyclotrons: I I poor RF sources; electron tube technology was yet in its infancy. relativistic increase of particle mass → decrease of ωc → asynchronism with RF Betatrons: I I intensity of trapped beam depends critically on the injected beam’s positions and angles. analysis of transverse oscillations of particles led to the theory of betatron oscillations of today. Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart DC high voltage generators Use of magnetic induction: betatron Drift tube linac and cyclotron Great progress just after world war II Advances during World War II (1941 - 1945) I High power microwave tubes for the radars were put to practical use I I magnetrons and klystrons Discovery of the phase stability principle in RF acceleration I Vladimir Veksler (1944) and Edwin M. McMillan (1945) I cyclotron → synchrocyclotron → synchrotron Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues The Principle of Phase Stability I Particles of different energies have I I I I I I differences in velocity and in orbit length; then, particles may be asynchronous with the RF frequency. The RF field, however, may have a restoring force at a certain phase, around which asynchronous particles be captured, that is to say bunched. This enables a stable, continuous acceleration of the whole particles in a bunch to high energies. Circular accelerators based on this principle are called “synchrotron.” This principle is also applicable to linacs, particularly in low energy range, to bunch continuous beams emitted from a source and to lead bunches to downstream accelerator sections. Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Synchrotron Oscillation (1) I Assume a sinusoidal RF electric field in an RF cavity gap: V = V0 sin ωt . I Assume a synchronous particle pass the gap center at ωt = 0, 2π, 4π, . . . and its acceleration voltage be Va (< V0 ). I Then in one RF period, there are there are two ϕ’s which satisfy Va = V0 sin ϕ. Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Sinusoidal RF Wave V0 Va 0 π/2 π φ -V0 Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Synchrotron Oscillation (2) I Only one of the two ϕ’s can capture particles, which make oscillations around the phase. I These oscillations are called synchrotron oscillation and the phase is the synchronous phase ϕs . I Which one is the ϕs depends on that the revolution time is longer or shorter for a energy deviation ∆E(> 0) from the synchronous energy. Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Synchrotron Oscillation in an RF Bucket (1) For the case of ϕs = 30◦ abscissa : ∆ϕ = ϕbeam − ϕs , ordinate : ∆E = Ebeam − Es Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Synchrotron Oscillation in an RF Bucket (2) For the case of ϕs = 0◦ abscissa : ∆ϕ = ϕbeam − ϕs , ordinate : ∆E = Ebeam − Es 2 1 3 2 -3 -2 -1 1 2 3 1 -1 -3 -2 -1 1 2 3 -2 -1 -2 -3 time sequence of motion of particles initially on the abscissa (particles of a larger ∆ϕ move slower or have a smaller ωs ) Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Advances in Beam Focusing Technique I Magnetic, not electric, focusing for high energy particles I Weak focusing in early cyclotrons and betatrons I Strong focusing I Nicholas C. Christofilos (1950) I Ernest D. Courant, M. Stanley Livingston, and Hartland S. Snyder (1952) Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Equation of Motion I In electric field E and magnetic field B, the equation motion of a particle is dp = e (E + v × B) dt where p = mv = γm0 v with m0 : rest mass √ γ = 1/ 1 − β 2 : Lorentz factor β = |v| /c = v/c Fundamental Concepts of Particle Accelerators Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Coordinate System I I In the analysis of beam focusing, it is usually important to describe the equation of motion of particles only for small deviations x and y along the path s of the reference orbit of a synchronous particle Thus, a Frenet-Serret frame with respect to the reference orbit is preferred: I I I unit vector tangent to the curve, unit vector in the direction of curvature, and the cross product of the them. y particle ρ x s tangent at s reference orbit Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Typical Weak-Focusing Magnetic Field Cylindrically symmetric magnet poles and magnetic fields of the early cyclotrons z 0 r Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Betatron Oscillations : Weak Focusing I First order approximation of the field pattern of the previous page ( ) ( ) x y By = B0 1 − n + . . . and Bx = B0 −n + . . . , ρ ρ where n = I dBy dρ By / ρ : the n value Equation of motion d2 x 1 − n + x=0 ds2 ρ2 I I and d2 y n + 2y = 0 2 ds ρ Focusing both horizontally and vertically → 0 < n < 1 Betatron wavelength √ λβ,x = 2πρ/ 1 − n √ λβ,y = 2πρ/ n Fundamental Concepts of Particle Accelerators Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Quadrupole Magnetic Fields for Stronger Focusing I I I No limitations for the n value. Focusing in one direction, defocusing in the other. Later we will see the focusing is superior to the defocusing y 2 1 -2 -1 1 2 x -1 -2 Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Q magnets and B magnets of JPARC RCS synchrotron (1) http://j-parc.jp/Acc/en/index.html Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Q magnets and B magnets of JPARC RCS synchrotron (2) http://j-parc.jp/Acc/en/index.html Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Q magnets and B magnets of JPARC Main Ring (1) http://j-parc.jp/Acc/en/index.html Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Q magnets and B magnets of JPARC Main Ring (2) Sextupole magnets are sometimes used. http://j-parc.jp/Acc/en/index.html Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Optical Lens Equivalent of a Quadrupole Magnet convex lens in one direction and concave lens in the perpendicular direction beam Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Strong Focusing with a Standard FODO Array F : focusing Q, D : defocusing Q, O : drift section vspace3mm I In the following figure, convex lenses are for horizontal focusing and concave lenses for vertical focusing. I The red curves are beam envelopes for a unit emittance. 1 0.5 0.5 1 1.5 2 2.5 3 -0.5 -1 Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Emittance Ellipse for a periodic sequence of Q magnets x! /k ag replacements #0 #1 #2 #3 0 -1 x/x0 1 0.5 0.5 #4 #5 #6 x′2 x2 + 2 = x20 k √ where 1 k= L L f ( L 1− 4f ) Concepts focusing of Particle Accelerators f : focal length, L : length betweenFundamental neighboring Q’s The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Betatron Oscillations : Strong Focusing (1) I Use quadrupole magnets with |n| ≫ 1, but with changing the sign of n alternatively I Equation of motion d2 x + Kx (s) x = 0 ds2 d2 y + Ky (s) y = 0 ds2 I Focusing/Defocusing forces Kx (s) and Ky (s) are periodic functions for the ring circumference L. I They are Mathieu-Hill type functions Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Betatron Oscillations : Strong Focusing (2) I General solution:x = Ax for y) I I I I √ β(s) cos (ψ(s) − ψ0 ) (similar too Ax and Ay are constants proper to each particles and are independent of the position s on the orbit 4 + β ′2 2 A2x = x − β ′ βxx′ + βx′2 4β measure a particular particle’s (x, x′ ) or (y, y ′ ) for many turns at a position s, the points trace an ellipse on the corresponding phase space. ellipse’s direction and eccentricity are functions of s, but area= πA2x (y) is conserved the largest area is, roughly speaking, called the emittance of the bunch Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Betatron Oscillations : Strong Focusing (3) I Beta function βx (y) (s) is defined as the betatron amplitude for Ax (y) = 1 : 2ββ ′′ − β ′2 + 4β 2 K (s) = 4. I Phase ψ of betatron oscillation : ∫ s ψ= ds/β. I Wavelength λβ of the betatron oscillation : the length corresponding the phase advance ∆ψ = 2π. I Betatron tune νβ ≡ L/λβ . Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Colliders (1) I In order to observe the high energy particle reactions : targets in laboratory frame were solely used (fixed target experiment). I The reaction, however, depends not on the laboratory energy of the projectile from an accelerator, but on the center of mass energy of the projectile and target. I Touschek’ idea to use colliding beams (1960) I The first collider:AdA (Frascati, 1961) 200 MeV e− ⇒⇐ 200 MeV e+ I The collider has become a paradigm of high energy accelerators of today. Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Colliders (2) : ECM I Consider collision of particles of the same rest mass m0 . I In a fixed target case with the projectile accelerated to γm0 c2 I I the total energy: ET /m0 c2 = (γ + 1) I the total momentum: pT /m0 c = βγ = I since E 2 − c2 p2 is a Lorentz invariant, √ √ ECM /m0 c2 = 2γ + 2 ≈ 2γ √ γ2 − 1 In a collision of two particles of the same energy γm0 c2 ECM /m0 c2 = ET /m0 c2 = 2γ Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Colliders (3) : Luminosity I For reaction cross section σ and beam cross section at the collision point S, the probability of reaction for a pair of particles is, σ S I Hence the probability for N+ and N− particles at a rate of f times per second σ f × N + × N− × S I Coefficient of σ is the luminosity L N+ × N − L=f× S Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Synchrotron Radiation (1) I The synchrotro radiation, SR, is an electric dipole radiation from a charged particle in acceleration v̇ I Radiation power in the rest frame is given by Larmour’s formula ( ) ( )2 2re me dv 2 2re dp P = = 3c dt 3me c dt where re ≡ e2 /(4πε0 me c2 ) = 2.82 × 10−15 m is the electron’s classical radius. Fundamental Concepts of Particle Accelerators Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart PSfrag replacements Electric Dipole Radiation : Electric Field Pattern #0 #1 #2 #3 Radiation pattern (cylindrically symmetric) of #4 #5 an electric dipole at rest#6 x/xz/λ 0 xe /x0 x! /k 4 η (m) s=0 s = 0 + nL 2 s = L2 s = L4 s = 0+ + nL r/λ s = 0+ 0 s = 0+ s = L + nL = 0 + (n + 1)L − − s/L-2 s (m) f = 1.6L ρ = 50 m -4 L=2m 0 1 2 3 4 5 Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Synchrotron Radiation (2) I Since P is the ratio of radiated energy to elapsed time, both of which transform in the same manner under Lorentz transformations, P must be an invariant. I Then ( )2 in the right hand side of the equation should have the following invariant form (dp/ds)2 − (dE/ds)2 /c2 where ds is the differential of proper time √ ds = dt2 − (dx2 + dy 2 + dz 2 ) /c2 = dt/γ. Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Synchrotron Radiation (3) I Hence in laboratory frame the radiated power is {[ ] [ ] } d (γc) 2 2re me 2 d (γv) 2 γ − P = 3c dt dt I The radiated energy per turn ∆E for a ring with radius ρ ∆E 4π re 3 4 = β γ 2 me c 3 ρ I A practical formula for ∆E(keV), E(GeV) and ρ(m) ∆E(keV) ≈ 88.5 [E(GeV)]4 /ρ(m). Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Synchrotron Radiation (4) I I I Pattern of electric dipole radiation in electron’s rest frame (x′ , y ′ , z ′ , ct′ ) dP/dΩ ∝ sin2 θ where Ω being the solid angle and θ the angle from z ′ axis. Transformation to laboratory frame x′ = x, y ′ = y, z ′ = γ (z − vt) , ct′ = γ (ct − vz/c) . Angles of axes x′ and y ′ with respect to z axis are ∼ 1/γ. I I I I forward radiation power is within a cone of a full angle of ∼ 2/γ. electron is observable for an arc length of ∼ 2ρ/γ. doppler effect shortens the wavelength by (1 − v/c) ∼ 1/2γ 2 . Critical wavelength (Schwinger-Jackson’s definition) λc ≡ 4πρ/3γ 3 Fundamental Concepts of Particle Accelerators Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Accelerating Cavity (1) There are many types of accelerating cavity, which, however, basically are variations of a cylindrical cavity (or pillbox cavity), operating on the fundamental TM010 mode. Hθ Ez b r= 2b 0 arbitrary scale I 1 Ez 0.8 Hθ 0.6 0.4 0.2 0 0.5 1 1.5 2 χ01r/b d Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Accelerating Cavity (2) Single-Cell Accelerating Cavity for Photon Factory Storage Ring (fRF = 500 MHz, Vpeak = 0.7 MV ) r R10mm R234.69mm Ez (r=0) R91.375mm R50mm z 220mm R130mm 300mm Fundamental Concepts of Particle Accelerators Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Accelerating Cavity (3) Global behavior of a resonant cavity is well described by an equivalent circuit comprising three parameters L, C, R. L R C Fundamental Concepts of Particle Accelerators Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Accelerating Cavity (4) I I I I first of all, the resonant frequency and the Q value are derived from the following two equations : √ ω0 = 1/ LC and Q = ω0 RC. one more independent relation is required to determine the three parameters L, C, andR. for this sake, we choose the peak acceleration voltage along the beam orbit this choice is reasonable, because it satisfies the energy conservation of the(EM fields + beam)system. ∫∫∫ ∫∫ J · EdV + (E × H) · ndS = 0. V S (J : beam current distribution, E × H : Poynting vector, V : cavity volume, S : cavity surface) Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues High Gradient Electric Fields and Breakdown I Kilpatrick’s empirical rule I Fowler-Nordheim’s theory for field emission I Surface damage on an X-band copper structure I Weak discharge: multipacting Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Kilpatrick Criterion W. D. Kilpatrick, Rev. Sci. Instr. 28 (1957) 824 Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Fowler-Nordheim’s Law R. H. Fowler and L. Nordheim, Proc. Roy. Soc. A 119 (1928) 173 J. W. Wang and G. A. Loew, SLAC-PUB-7684 (1997) I DC field emission current density jF [A/m2 ] : ( ) −0.5 1.54 × 10−6 × 104.52ϕ E 2 6.53 × 109 ϕ1.5 exp − jF = ϕ E I I microscopic surface gradient E [V/m] metal work function ϕ [eV] I Averaged over one RF cycle, jF is modified as: ( ) −0.5 6.53 × 109 ϕ1.5 5.7 × 10−12 × 104.52ϕ E 2.5 exp − jF = ϕ1.75 E I Field enhancement factor β : E = βEmacro Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Surface Damage on the Iris of an X-band Linac Structure R. E. Kirby, SLAC-PEL, 2000 Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Multipacting : a weak discharge phenomenon A. J. Hatch and H. B. Williams, Phys. Rev. 112 (1958) 581 Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Superconductor and RF I Niobium is mostly used, which is a Type II superconductor I I I I I critical temperature Tc = 9.2K critical field Hc = 2 × 103 Oe in meissner state for H ≤ Hc1 = 1.7 × 103 Oe in normal state for H ≥ Hc2 = 2.3 × 103 Oe Maxwell equations + London equations I London’s penetration depth λL • about 50 nm for niobium I coherent length ξ0 • about 40 nm for niobium I wall losses do still exist, although very small, which are caused by normal electrons Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Equations for Superconducting State I Maxwell’s equations: ∇×E+ I ∂B =0 ∂t and ∇ × H − ∂D =J ∂t London equations: Js = −j ns e2 ns e2 E and ∇ × Js = − µ0 H ωme me I Field equations: I ( ) 2 ∇2 (J, E, H) = λ−2 L + jωσµ0 − ω ε0 µ0 (J, E, H) √ London’s penetration depth: λL = me /ns e2 µ0 Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues Klystron (1) I Also an accelerator with decelerating electric fields I Perveance µp I Child-Langumuir law for space-charge limited flow • µp ∝ I/V 3/2 • cf. M. Reiser: Theory and Design of Charged Particle Beams, John Wiley & Sons, 1994. I Efficiency vs. perveance I cf. R. B. Palmer and R. Miller: SLAC-PUB-4706, September 1988. Fundamental Concepts of Particle Accelerators Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Klystron (2) GULIWWXEH FHUDPLFEXVKLQJ LQSXW FDYLW\ ZHKQHOWHOHFWURGH IRFXVLQJ PDJQHW DPSOLI\LQJ FDYLW\ RXWSXWFDYLW\ FROOHFWRU +9 KHDWHU FDWKRGH DQRGH FHUDPLF ZLQGRZ 5)LQSXW FHUDPLF ZLQGRZ EHDP 5)RXWSXW Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Principle of RF phase stability Strong focusing collider synchrotron radiation (SR) Technical issues 500 MHz-1 MW CW Klystron for KEKB Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Future Accelerators I ERL: Energy Recovery Linac I LC : Linear Collider I µ-µ Collider and/or µ-Factory I Laser-plasma acceleration Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart KEK-PF-ERL : A Future Plan I An SR source with a superconducting linac energy-recovered by returned electron beams Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Linear Collider: schematic layout Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart µ-µ Collider /LQDF /L%H$EVRUEHUV 6\QFKURWURQ 3URWRQ /LQDFV &ROOLGHU M 7DUJHW 6ROHQRLG 5HFLUFXODWLRQ M /LQDF /LQDF Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Laser Plasma Acceleration (1) cf. C. Joshi and T. Katsouleas’s article in Physics Today, June 2003, p.47. Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Laser Plasma Acceleration (2) Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart Livingston Chart I Originally given by M. S. Livingston & J. P. Blewett: ”Particle Accelerators, p.6”, MacGraw Hill, 1962 Collider (Equivalent Energy) I Proton Synchrotron I Energies for the colliders are equivalent values for the fixed target system Maximum beam energy ever achieved 17 10 16 10 15 10 1PeV Ac ce l er at or E nerg y ( eV) 1014 13 10 12 10 1TeV 11 10 Electron Linac I 10 10 10 9 10 8 10 7 10 6 Electron Synchrotron Synchro-cyclotron 1GeV I Proton Linac 1MeV 1930 Electrostatic Accelerator Betatron Cyclotron DC Generator 1940 1950 1960 1970 1980 1990 2000 2010 I Electron Synchrotron : 2 × 100 GeV (2000, CERN LEP) Proton Synchrotron : 2 × 7 TeV (2010, CERN LHC) http://lhc.web.cern.ch/lhc/ Electron-positron linear collider 2 × 500 GeV? (2025 or later?) Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart References (1) I Segrè, E. : From X-rays to Quarks (W. H. Freeman and Company, 1980). I I Chao, A. W. and Tigner, M. (ed.) : Handbook of Accelerator Physics and Engineering (World Scientific, 1999). I I Compact encyclopedia of accelerator science and technology Wiedemann, H. : Particle Accelerator Physics I, II (Springer, 1999). I I Historical introduction to the evolution of high energy physics and accelerator science Text book on accelerator physics Courant, E. D. and Snyder, H. S.: Annals of Physics, 3 (1958) p.1. I A classical paper on the theory of the strong focusing Fundamental Concepts of Particle Accelerators The Dawn of Particle Accelerator Technology Basic Concepts Accelerators in Future Livingston Chart References (2) I Schwinger, J. : Physical Review, 75 (1949) p.1912. I I Gilmour, A. S. : Microwave Tubes (Artech House, 1986). I I A classical paper on the theory of the synchrotron radiation Text book on the electron tube technology Padamsee, H., Knobloch, J. and Hays, T. : RF Superconductivity for Accelerators (John Wiley & Sons, 1998). I Text book on RF superconductivity and its application to energy accelerators Fundamental Concepts of Particle Accelerators