Accelerators We’ve seen a number of examples of technology transfer

Accelerators We’ve seen a number of examples of technology transfer in particle detector development from HEP (basic science) to industry (medical, ) Particle accelerators provide another such example There are currently more than 30,000 particle accelerators in use throughout the world with only a small fraction being used in HEP/nuclear research 1

Accelerators Circa 2000 2

Accelerators A brief history 3

Accelerators A brief history Electrostatic (Cockcroft-Walton, van de Graaf) Linac (linear accelerator) Circular (cyclotron, betatron, synchrotron) Development of strong focusing Colliding beams (present day) Plasma wakefield, ? 4

Accelerators “Moore’s law” e t/C 5

Accelerators “Moore’s law” 6

Linac Linac linear accelerator Applications in both high energy physics and radiation therapy 7

Linac Linacs are single pass accelerators for electrons, protons, or heavy ions Thus the KE of the beam is limited by length of the accelerator Medical (4-25 MeV) – 0.5-1.5 m SLAC (50 GeV) – 3.2 km ILC (250 GeV) - 11 km Linac – static field, induction (time varying B field), RF Operate in the microwave region Typical RF for medical linacs 2.8 GHz Typical accelerating gradients are 1 MV/m – 100 MV/m 8

Linac Brief history Invented by Wideroe (Germany) in 1928 Accelerated potassium ions to 50 keV using 1 MHz AC First realization of a linac by Sloan (USA) in 1931 No further progress until post-WWII when high power RF generators became available Modern design of enclosing drift tubes in a cavity (resonator) developed by Alvarez (USA) Accelerated 32 MeV protons in 1946 using 200 MHz 12 m long linac Electron linac developed by Hansen and Ginzton (at Stanford) around the same period Evolved into SLAC laboratory and led to the birth of medical linacs (Kaplan and Varian Medical Systems) 9

Linac Wideroe’s linac 10

Linac Alvarez drift tube linac First stage of Fermilab linac 11

Linac A linac uses an oscillating EM field in a resonant cavity or waveguide in order to accelerate particles Why not just use EM field in free space to produce acceleration? We need a metal cavity (boundary conditions) to produce a configuration of waves that is useful Standing wave structures Traveling wave structures 12

LINAC Medical linacs can be either type 13

Waveguides Recall some of Maxwell's equations d SB da 0 and LE dl dt SB da At a boundary between different media BT1 BT2 0 and E 1 E 2 0 In a metal cavity, the following boundary conditions apply E BT 0 at the metal wall We distinguis h two sets of solutions TM mode E z 0 TE mode Bz 0 TEM mode cannot occur 14

Waveguides Cyclindrical wave guide Consider a cylindrical wave guide of radius a Consider the TM modes B z 0 The z component of the E field is given by E z r , E0 J m kc r e i t kz m The metallic boundaries are at the zero' s of the Bessel functions We also have k 2 k x2 k y2 k z2 kc2 k z2 If k z is real, the wave propagates If k z is imaginary, the wave falls off exponentially The cutoff wavenumber k c is determined by the waveguide dimensions 15

TM Modes TM01 mode 16

Waveguides The phase velocity is given by v ph k v ph c kz k No problem that v c since no information or energy is transmitted But there is a problem in that no acceleration is possible d 2 v gr c 1 c / c dk 17

Waveguides Phase and group velocity 18

Waveguides Phase and group velocity E E0 sin k dk x w d t E0 sin k dk x w d t E 2 E0 sin kx t cos dkx d t E 2 E0 f1 x, t f 2 x, t The phase of the first term is propagated so that kx t is constant The phase velocity is v p k The second term defines the envelope and again the phase of this term is propagated so that xdk td remains constant d The group velocity is v g dk Information or energy is propagated with the group velocity 19

Waveguides The phase velocity can be slowed by fitting the guide with conducting irises or discs The derivation is complicated but alternatively think of the waveguide as a 1 v ph line transmission LC 0 0 Conducting irises in a waveguide in TM0,1 mode act as discrete capacitors with 1 v ph d in parallel with C0 separation L0 C0 C / d 20

Waveguides Disc loaded waveguide 21

Traveling Wave Linac Notes Injection energy of electrons at 50 kV (v 0.4c) The electrons become relativistic in the first portion of the waveguide The first section of the waveguide is described as the buncher section where electrons are accelerated/deaccelerated The final energy is determined by the length of the waveguide In a traveling wave system, the microwaves must enter the waveguide at the electron gun end and must either pass out at the high energy end or be absorbed without reflection 22

Traveling Wave Linac 23

Standing Wave Linac Notes In this case one terminates the waveguide with a conducting disc thus causing a /2 reflection Standing waves form in the cavities (antinodes and nodes) Particles will gain or receive zero energy in alternating cavities Moreover, since the node cavities don’t contribute to the energy, these cavities can be moved off to the side (side coupling) The RF power can be supplied to any cavity Standing wave linacs are shorter than traveling wave linacs because of the side coupling and also because the electric field is not attenuated 24

Standing Wave Linac 25

Standing Wave Linac Side coupled cavities 26

Electron Source Based on thermionic emission Cathode must be insulated because waveguide is at ground Dose rate can be regulated controlling the cathode temperature Direct or indirect heating The latter does not allow quick changes of electron emission but has a longer lifetime 27

RF Generation Magnetron As seen in your microwave oven! Operation Central cathode that also serves as filament Magnetic field causes electrons to spiral outward As the electrons pass the cavity they induce a resonant, RF field in the cavity through the oscillation of charges around the cavity The RF field can then be extracted with a short antenna attached to one of the spokes 28

RF Generation Magnetron 29

RF Generation Magnetron 30

RF Generation Klystron Used in HEP and 6 MeV medical linacs Operation – effectively an RF amplifier DC beam produced at high voltage Low power RF excites input cavity Electrons are accelerated or deaccelerated in the input cavity Velocity modulation becomes time modulation during drift Bunched beam excites output cavity Spent beam is stopped 31

RF Generation Klystron 32

Medical Linac Block diagram Electron source Bending magnet Accelerating structure Pulse modulator Klystron or magnetron Treatment head 33

Medical Linac 34

Medical Linac 35

Cyclotron The first circular accelerator was the cyclotron Developed by Lawrence in 1931 (for 25) Grad student Livingston built it for his thesis About 4 inches in diameter 36

Cyclotron Principle of operation Particle acceleration is achieved using an RF field between “dees” with a constant magnetic field to guide the particles 37

Cyclotron Principle of operation mv 2 qvB for v c mv p B e e Note that the frequency remains constant as the particle is accelerate d v v eB eB f 2 2 mv 2 m Limited by relativity since v in velocity and momentum won' t cancel as v approaches c 38

Cyclotron Why don’t the particles hit the pole pieces? The fringe field (gradient) provides vertical and (less obviously) horizontal focusing 39

Cyclotron TRIUMF in Canada has the world’s largest cyclotron 40

Cyclotron TRIUMF 41

Cyclotron NSCL cyclotron at Michigan State 42

Cyclotron 43

Betatron Since electrons quickly become relativistic they could not be accelerated in cyclotrons Kerst and Serber invented the betatron for this purpose (1940) Principle of operation Electrons are accelerated with induced electric fields produced by changing magnetic fields (Faraday’s law) The magnetic field also served to guide the particles and its gradients provided focusing 44

Betatron Principle of operation Steel B0 Coil B Vacuum chamber Bguide 1/2 Baverage 45

Betatron Principle of operation A requirement for the B field of the betatron is B Borbit 2 d dB Emf A dt dt 2 dB E 2 R R dt R dB E 2 dt The force on the electron is then dp eR dB dt 2 dt eRB p eRBorbit 2 F 46

TM Modes 47

TE Modes Dipole mode Quadrupole mode used in RFQ’s 48

Waveguides 2 m ,i 2 Note when , then k is imaginary a and the wave no longer propagates Also note 0,1 2.405 2 2 c 2 c 2 a Thus c 2.61a c 2.405 So the cavity radius determines the wavelength For a 10 cm, λ 26 cm and f 1.15 GHz 49