General Introduction to Particle Accelerator Systems

Soken-dai Core Curriculum, Fall, 2020 Introduction to Accelerators II - Week 1

2020/10/15

Nobukazu Toge (KEK) Nobu.toge@kek.jp 1 What this Lecture is for

• This lecture:

– Gives you a cursory overview of various accelerator systems, their subsystems and components via a short walk-through seminar in the class,

– Helps you (hopefully) acquire some sense of how a real-life accelerator is like.

2 Texbooks

• Introductory textbooks which might benefit you are as follows:

– S.Y.Lee: Accelerator Physics, World Scientific, 2004. Many of its chapters are available for viewing online: http://bit.ly/93zVw6

– D.Edwards and M.Syphers: AIP Conf. Proc. 184, 1989, American Institute of Physics

– H.Wiedemann: Particle Accelerator Physics, Springer Verlag, 1993.

– OHO Lecture Series (although they are mostly in Japanese).

– A.Chao and M.Tigner: Handbook of Accelerator Physics and Engineering, World Scientific, 1999.

3 Particle Accelerator

• Particle beamsSituation where a group of electrically charged (or neutral) particles are moving at mostly the same velocity (momentum) in mostly the same direction.

• Particle accelerators: Set of instruments which creates particle beams artificially in a controlled manner.

• Use of particle beams: Particle beams may be used as they are, or may be used to create other secondary beams for - – Experimental research in particle physics, nuclear sciences, materials and life sciences, and/or – Medical and industrial application with their capacity of penetrating, imaging and processing materials

4 Particle Accelerator

– Human control ! Allows experiments under controlled conditions (Exemplary experimental sciences, with benefits and limitations. – How many Nobel prizes where experiments with particle accelerators played decisive roles? Ans11 cases out of 139: 21 winners out of 217, as of Fall, 2020

• Particle accelerators are a subject of research and development on their own – New regimes of particle energies or particle numbers can be realized only by the efforts of accelerator builders – you have to do it yourseves. – It of course, means collaborative work with other fields and industries is essential – you have to work with other people.

5 Real Basics

• Energy / Momentum 1 – Non-relativistic: E = mv2 ; p = mv 2

– Relativistic: E = m2c4 + p2c2 = mc2g ; p = mcgb b = v / c; g =1/ 1- b 2

– Speed of light: c = 2.9979 108 m/s ! ! ! ! – Forces on charged particles: F = q(E + v ´ B)

– And when the B is UP, the electrons go to the LEFT. – Unit of energy: eV (electron-volt) keV (103), MeV (106), GeV (109), TeV (1012) Unit of momentum: eV/c (electron-volt/c)

6 Particle Acceleration

• It means to increase the kinetic energy of a particle. • Charged particle attains an additional kinetic energy as it passes through a space with electric field • Electron Volt – 1eV = Kinetic energy attained across a potential gap of 1V Electric charge of an electron = 1.602 10^-19 C 1 eV = 1.602 10^-19 J – Velocity of an electron with kinetic energy 1eV ? E = mv^2/2, where an electron mass m = 9.1 10^-31 kg , 1 eV = 1.602 10^-19 = 9.1 10^-31 v^2 / 2 v = 5.9 10^5 m/s v/c = 5.9 10^5 / 2.9979 10^8 = 0.002 Velocify of a proton with kinetic energy 1000 eV ?

Mainly electrons and positrons

Belle-II Detector SuperKEKB

Photon Factory Slow e+ facility

e-/e+ Linac

8 Linear accelerator for e- and e+ KEK Tsukuba

9 Linear accelerator for e- and e+ KEK Tsukuba

10 Accelerator System - SuperKEKB Straight Section http://www-acc.kek.jp/KEKB/index.html Detector Facility for HEP Experiment

Bending Section

Accelerator Cavities

Positron Damping Ring Linear Accelerator (Linac) Positron Source

Electron Source Linear Accelerator (Linac) Counter-travelling e- (7GeV; Blue) and e+ (4GeV; Red) beams are made to collide repeatedly at a single collision point – Goal: Max the particle collision rate. 11 Accelerator System - KEKB

12 First hadronic event that was observed at Belle-II (April 26, 2018)

Belle-II detector at SuperKEKB 13 Accelerator System – Light Source Rings http://pfwww.kek.jp/outline/pf/pf1.html

PF Ring (2.5 – 3GeV) AR Ring (6 – 6.5 GeV)

Store only the electrons to produce SR light (X-rays) for experiments. Goal: Max support user experiments with SR of desired characteristics.

Hard X-ray stations Soft X-ray stations 14 Accelerator System – Light Source Rings

Exp hall at the KEK Photon Factory

15 Accelerator System – Energy Recovery Linac (ERL) http://pfwww.kek.jp/ERLoffice/ ERL is similar to light source rings in that it utilizes light emission off electron beam as it goes through undulator Beam dump magnets. Differences (and advantages), however, include: + one-time use of beam, i.e like linear Accelerator Cavities accelerator (Superconducting) + opportunities for very bright, very short light pulses + energy recovery

Undulator magnets as light source

Injector “CompactERL” prototype E ~ 35-245 MeV; I ~ 10 mA; ge ~ 0.1 – 1 mm ; st ~ 100fs rms Proposal for “Real” ERL

Electron source E ~ 5GeV; I ~ 10 - 100mA ; ge ~ 10 – 100 pm; st < 100fs rms 16 Accelerators at KEK Tsukuba

Facility Primary Beam Use Application SuperKEKB Electron, Collision High energy physics Positron PF Electron Synchrotron radiation Material + life sciences PF/AR Electron Synchrotron radiation

Electron, Positron Electron, Delivery to SuperKEKB, PF, PF/AR Injector Positron

CompactERL Electron Synchrotron radiation R&D of new SR source ATF Electron Beam studies R&D of Beam handling for ILC STF Electron SRF cavity R&D R&D for SRF beam acceleration

17 Accelerator System – J-Parc http://www.j-parc.jp 3GeV Synchrotron 50GeV Synchrotron – 15µA (0.4 ! 3GeV; 333µA 1MW, 25Hz) Hadron Exp Mat / Life-science exp Accelerator-Driven Transmutation Fac.

Linac (0.4-0.6GeV; Neutrino Exp Fac. 15µA, 500µs, 50Hz) To Super-Kamiokande High-power proton accelerator to concurrently support numerous user experiments spanning over material / life / nuclear and particle. Goal: Reliable delivery of high-current proton beams. 18 Accelerator System – J-Parc

19 T2K Experiment (T2K = Tokai ! Kamioka)

20 Accelerators at J-PARCKEK + JAEA of Tokai Facility Primary beam Beam usage Application Proton linac Proton Delivery to RCS, MR RCS Proton Delivery to MLF to Material and life produce neutrons sciences and muons Delivery to MR MR Proton Delivery to hadron High energy physics facility (HF) to and nuclear physics produce mesons and muobns Proton Delivery to neutrino High energy physics production beamline ! SuperKamiokande

21 Accelerator System – Linear Collider https://www2.kek.jp/ilc/ja/

250GeV e- on 250GeV e+; Rep rate = 5Hz

Accelerate electron beam and positron beam with two linear accelerators, and have them collide head-on at the beam collision point at the center for experiments in HEP. Goal: Max the energy reach, max the beam interaction rate. Check the movie at http://bit.ly/dutCx0 for visual effects. 22 Basics (1)

• Energy and momentum of material particles: – Non-relativistic case, where velocity v is much smaller than speed of light c - 1 E = mv2 ; p = mv 2

– Relativistic case: E = m2c4 + p2c2 = mc2g = mc2 / 1- b 2 p = mcgb = mcb / 1- b 2

Where,

b = v / c; g =1/ 1- b 2 – Speed of light: c = 2.9979 108 m/s

23 Basics (2)

• Simplified special relativity ! # ! = , # = " #$%!

$ = %&&#

Knowing 1 ! = 1 − #&

%! If ) ≪ & ,γ ~ 1 + . So, & !& 1 $~%&& 1 + = %&& + %)& 2 2 24 Basics (3)

• In our field the particle masses are measured in the unit of energy

Rest mass energy = %&& For electrons: %&& = 9.109 2 10$'# (2.9979 2 10()& = 8.19 2 10$#) J 1eV = 1.602 10-19 J Rest mass energy of an electron is %&& = 8.19 2 10$#)/1.602 2 10$#* = 5.11 2 10) = 511 keV

Velocity of an 8GeV electron? γ = 8 2 10+/511 2 10' = 1.5656 2 10) 1 1 ! = 1 − ~1 − = 1 − 2 2 10$+ #& 2#& 25 Basics (4) If the B field is “up” an electron goes LEFT

Equation rofgives circular the motion. radius of curvature of the trajectory.

26 Creating a particle beam?

• Electrons and protons are abundant in materials. Yet they are usually in bound states.

• To create electron/proton beams means – To unbound them, and – To bring them into the state suitable for handling with particle accelerators.

• Particles which don’t exist naturally (for instance, positrons) need to be artificially created.

27 Electron Source (Example)

Thermionic Gun: Thermal electrons are extracted from a cathode which is set at a negative HV and is being heated.

Electrons

28 29 Electron source2

30 RF electron gun for the electron/positron linac at KEK Tsukuba. Positron source

Bring high energy electron or photon beams on high- intensity target (tungsten etc) and let them produce electromagnetic showers.

Pick up positrons produced in e+e- pair creation (threshold energy = 2 x 511keV)

31 Flux concentrator in construction / testing

32 Positron Source

• Flux Concentrator (FC) is a device which is used as OMD (Optical Matching Device) in a positron production system. FC can produce strongly focused ~solenoid field (6- 10T) out of eddy current that is induced by pulsed primary coil current on its outside. However, FC, generally is limited in its pulse length (< 30 µs).

T.Kamitani • Other devices to use as OMD include: – AMD (adiabatic matching device) – a solenoid magnet with adiabatically changing field strength; – QWT (quarter-wavelength transformer) – a short strong solenoid followed by a weaker solenoid; – LL (Lithium lens). They can replace FC for longer pulses but at lower magnetic field, or require additional R&D. Positron production system at the KEK electron/positron injector linac.

34 Proton Source

• Out of H2, you can either create p or H-, but for – Ease of attaining a high current, and – Ease of handling during injection in the booster synchrotron, It is advantageous to use H- (p with two electrons) in the upstream end of a proton accelerator system. • J-PARC uses H- – Filament (TaB6) discharge H- source in a Plasma ch. ! – Extraction of H- via three sets of electrodes (50kV in total) ) – ! RF-Qs • Electrons can be stripped off H- easily later, when an accelerated H- passes through thin foils. H.Oguri et al 35 Advantage of H- for Injection into RCS (Rapid Cycling Synchrotron)

H- to inject

Foil

Proton in RCS

Dipole magnets

• Electrons can be stripped off H- easily when an accelerated H- passes through thin foils immediately after injection in RCS. • Radiation effect on and lifetime of the charge-conversion foils have to be dealt with, however. 36 Accelerator Subsystems – Particle Sources Particles Technique Note Ions / Protons Ionization / Plasma Both +/- Charges Anti-protons p-pbar production Thermionic Electrons Photo-cathode Polarized / Unpolarized Ultra-low emittance EM shower e- - initiated Positrons photon-initiated SR from orbit bending SR rings (high inten, low-emittance) Photons ERL (very short pulses) Compton scattering New light sources Nuclear reactor Slow Neutrons Proton on target Fast Hadrons (p, K, …) Proton on target Muons p, K decays Slow / Fast p, K decays Neutrinos Nuclear reactors 37 How to control the motion of charged particle beams? • Charged particles, – Once they are accelerated to certain energies, – Will continue straight motions unless they collide with other material particles. • To change their direction of motions, we use – Electric or magnetic fields – More often the magnetic fields for their ease of use.

38 Dipole Magnets

• Dipole magnets are the primary tools to control the orbit of beam particles. – Big dipole magnets to define the orbit are often called “bend magnets”. – Small dipole magnets for orbit correction are often called “correctors.” • Lorentz force formula: F = evB – Remember: When the field is UP, an electron goes to the left, a positron (or proton) goes to the right.

• Q4: Prove 3.3356p [GeV] = B [T] r [m]

Electron is going counter-clockwise in ATF Damping ring. Is the B field up or down? Dipole Magnets • Q5: Have a 0.3T magnet which is 5.804m long. What is the bending Dipole magnet with length (thickness) L, angle for a 8GeV beam? field B

• A5: Charged particle Use 3.3356p = Br ; Bending angle q r = 3.3356p / B Note: B in T, p in GeV/c Bend angle q = L/r = BL / 3.3356p Bending radius r Use, for instance, B = 0.3T p = 8GeV/c Bending angle q L = 5.804m q = 0.3 x 5.804 / 3.3356 x 8 = 0.06251rad This is actually the parameter r = 88.95m for the (previous) high-energy ring (HER) of KEKB Q5B: How many dipoles of this kind do you need to form a complete ring? 40 Dipole Magnets

Q6: LHC now has beam momentum 3.5 Q7: The LHC dipoles are actually running TeV. Ring circumference is 27km. What is at ~4.2T for 3.5TeV beam. What is the the required B, if the whole ring is “dipole packing factor?” completely packed by dipole magnets? A7: A6: • Remember, 3.3356p = Br • r = C / 2p • Bending radius in dipoles with B = 4.2T = 27000 / (2 x 3.14) would be = 4297.2 m r = 3.3356p / B • Remember, 3.3356p = Br = 3.3356 x 3.5e3 / 4.2 • B = 3.3356p / r = 2779.7 m = 3.3356 x 3.5e3 / 4297.2 • Total length to occupy with dipoles = 2.72T would be 2 p r = 2 x 3.14 x 2779.7 = 17.465 km • Packing factor = 17.5e3 / 27e3 = 65% (Actually LHC has 1232 units of dipoles, each 15m long) 41 y Quadrupole Magnets

• Quadrupole (quad) magnets are the primary tools for focusing the beam, or a for stabilizing the beam orbit around its x center.

• By = Gx; Bx = -Gy • G = field gradient [T/m] • If quad is focusing in x, it is defocusing in y. • Pole field is ~ 1.4× a G where “a” is the aperture radius of the magnet.

• Q8. Prove that a quadrupole magnet with field gradient G and length L would provide a particle of momentum p with a focal length F that is given by: F = 3.3356p / (GL)

ATF2 42 Quadrupole Magnets

A8.

x q

Focal length: F 3.3356 p x GL × x 3.3356 p Bend radius : r = F = = x / = Gx q 3.3356 p GL

L GL Bend angle =q = = x r 3.3356 p

43 Single-Particle Optics

• We saw that a thin quad magnet (GL) acts like • One sees that if there are no magnetic a focusing / defocusing lens with components along the beamline, after a length of s, the (x, x’) of the particle would F = 3.3356p/(GL). be like, What if you had a series of such magnets x(s) = x(0) + s x’(0) spaced apart by L ? x’(s) = x’(0)

(NB: That L is different from that within (GL); sorry about the confusing notation.) So in vector notation, æ x(s) ö æ1 söæ x(0) ö • Let us characterize the particle trajectory in x ç ÷ = ç ÷ç ÷ with a “vector” è x'(s)ø è0 1øè x'(0)ø (x, x’). • What is the effect of a thin quad (e.g. ignore x is the location of the particle and the thickness) with focal length F on (x, x’)? x’ is the angle of the trajectory, i.e. The quad does not change x, but does change x’ by x’ ! x’ – x/F x’ = dx / ds where s denotes the coordinate along the æ x ö æ 1 0öæ x ö canonical trajectory. ç ÷ = ç ÷ç ÷ è x'øafterQ è-1/ F 1øè x'øbeforeQ In the following discussion, we ignore particle acceleration for simplicity. We call matrices like these “beam transfer matrices”. Single-Particle Optics

• Consider a system that consists of • What if we had an N series of such a drift L (*not to mix with quad “cells”? ! It is equivalent to thickness!), a thin defoc quad (-F), considering MN. This issue is another drift L, a foc thin quad (F). considered more transparently if What is this system’s beam we ask help of engenvalues / transfer matrix M? vectors. ! ! Eigenvector :V ,V ù 1 2 ú of matrix M Eigenvalue: l1,l2 û Arbitrary vector can be decomposed as æ x(0) ö ! ! 1 0 1 L 1 0 1 L ç ÷ = c1V1 + c2V2 æ öæ öæ öæ ö ç x'(0)÷ M = ç ÷ç ÷ç ÷ç ÷ è ø è-1/ F 1øè0 1 øè1/ F 1øè0 1 ø N æ x ö 1 L 1 L Effect of M on ç ÷ would be æ öæ ö ç x'÷ = ç ÷ç ÷ è ø è-1/ F 1- L / F øè+1/ F 1+ L / F ø N æ x ö N ! N ! 2 æ1+ L / F 2L + L / F ö M ç ÷ = c1l1 V1 + c2l2 V2 = ç ÷ è x'ø ç 2 2 2 ÷ è - L / F 1- L / F - L / F ø 45 Single-Particle Optics

• So the question reduces to evaluating • So, if the eigenvalues of M. Recall the basic (Tr M / 2)2 < 1 linear algebra. -1 < 1 – L2/2F2 < 1, i.e. | L / 2F | < 1 Eigenvalues l1,l2 are solutions of M - lI = 0 Then the eigenvalues will be complex.

Thus, Since l1 l2 = 1, they can be written as 2 –iµ +iµ l -TrM ×l + M = 0 l1 = e , l2 = e and where, M =1. MN will not be divergent! so ! Principle of FoDo lattice.

l1 + l2 = TrM l l =1 Q9: We have magnets with G = 1T/m, 1 2 thickness 0.5m. Let us set the half cell N Hence, if l is real, M is divergent. length of FoDo to be 5m (full length 10m). For which momentum range can Note: det M = 1, because all the this beamline act as a non-divergent transfer matrices of the “components” FoDo? which contributed to M have their Q10: How would all the analysis above determinant 1. change, if we do NOT ignore the thickness of the quads? 46 FoDo Lattice Examples Beamline of ATF2

ATF damping ring

47 The Beam • How does one characterize the transverse spread of the beam, i.e. that of a group of many particles? – Consider an ensemble of particles with distributed (x, px), measured from the beam centroid.

– Take (x, px) as the canonically conjugate variables of motion, and take it that they consitute the “Phase Space” of the group of particles. – If acceleration is ignored, (x, x’) can serve the purpose instead of (x, px).

– Same goes for (y, py) and (z, E). • Systematic analysis of all these in practical beamlines requires much elaboration of single-particle motions, • So, take the area occupied by particles in starting from the previous pages. My the (x, x’) plane (it is a virtual plane) , and lecture cannot really cover this critical call it - “Beam Emittance in x”. topic at all! Trust that Ohmi san’s lecture – Dimension of transverse beam covers it in detail. emittance is, thus, (m), 48 Superconducting Magnets

• Iron saturates at ~ 2T. This gives limitation to the field strength achievable with normal-conducting iron- dominated (NC) magnets. For instance, dipole magnets with B > 1.5 T, or quadrupole magnets with a G > 1T (a is the “aperture” of the quad) should go “superconducting” (SC).

• SC magnets, without iron, can produce higher field. But, because of the absence of the iron poles, one has to carefully arrange the electric current distribution to produce the desired field pattern. ! Lecture by Tsuchiya

• SC magnets, with iron, is, again, limited in strength, similarly to NC magnets. However, they are substantially lower power consuming. QCS for SuperKEKB

50 Magnets - Comments

• Generally, Maxwell’s equation allows solutions of many higher order fields besides dipole and quadrupole fields (sextupole, octapole, decapole, dodecapole etc). • Such fields are sometimes useful for beam controls; They are also sometimes very harmful. • It is important to control the higher pole field. This leads to tolerance issues of the magnetic poles (NC) or current distribution (SC).

• Thermal effects and mechanical aspects are also important issues for practical magnet designs and operation.

• Survey and alignment of the magnets are critical tasks to do before starting operation of a new accelerator.

• Finally, magnet power supplies (settability, stability and lifetime) are a very important area which is sometimes overlooked. Particle Acceleration

• It means to increase the kinetic energy of a particle. • Charged particle attains an additional kinetic energy as it passes through a space with electric field • Electron Volt – 1eV = Kinetic energy attained across a potential gap of 1V Electric charge of an electron = 1.602 10^-19 C 1 eV = 1.602 10^-10 J – Velocity of an electron with kinetic energy 1eV ? E = mv^2/2, where an electron mass m = 9.1 10^-31 kg , 1 eV = 1.602 10^-19 = 9.1 10^-31 v^2 / 2 v = 5.9 10^5 m/s v/c = 5.9 10^5 / 2.9979 10^8 = 0.002 Velocify of a proton with kinetic energy 1000 eV ?

52 DC Acceleration Good for up to a few hundred KeV.

Cockroft-Walton accelerator. Cockroft-Walton generator circuit. KEK has one, too, for 12GeV protron synchroton, completed in 1976. 53 KEK’s Cockcroft-Walton Generator

54 Problem with DC acceleration

- Electrons as represented by the green bunch can be accelerated.

- Electrons as the red bunch cannot be accelerated.

- Generally it is near impossible to use DC electric field for repeated acceleration of the same bunch.

be Can be Cannot acceleraed accelerated

55 Repeated acceleration with AC field

Oscillating field - Problem with the DC field (impossibility of repeated particle acceleration) can be solved by

time t =0 - Use of alternating electric field whose polarity cycles between positive and negative at a certain period. Hollow metallic pipe - i.e. use of AC electric field.

- IFF the arrival of charged particles and the switching AC phase are in adequate synchronization.

Figs from M.W.Poole time t =½ of field cyecle - Of course, particle trajectories have to be suitably arranged. 56 Particle acceleration with AC field

N pole of a magnet Cyclotron:

For non-relativisitic velocity v, F = evB = mv2/r Mag field eB = mv / r

Period of circular motion of proton, T, Protons turns out to be constant T = 2 pr / v = 2 p m / eB

S pole of a magnet If the AC period and T are the same, repeated acceleration can be realized.

AC source

57 Early cyclotron in Japan

#2 cyclotron at RIKEN In 1943. Diameter of the magnet 150cm

58 Particle acceleration with AC field (2)

Wideroe accelerator (1928):

Drift tubes are alternatingly connected to a common AC source (microwave source). The lengths of the drift tubes are arranged longer and longer as the particle velocity inceases.

Quite effective for accelerating protons up to several hundred MeV

J-PARC Drift-Tube Linac (DTL)

59 Repeated acceleration

• To realize repeated acceleration, the AC field needs to be used with very accurate synchronization between

– Circular motion of particles (" particle path length / particle velocity) – Switching of accelerating field (" AC frequency and the phase)

Very important point. Otherwise, it won’t work.

• Control of all relevant parameters are a crucial issue.

60 Acceleration - Synchrotron

Bending magnets Accelerator (Dipole magnets) cavity When acceleration is desired, sweep the field strength of magnets in sync with acceleration.

When acceleration is not needed, maintain the constant field strength

Vacuum pipes

Focusing magnets (Quadrupole magnets) Note: 3.3356p (GeV/c) = B (T) r (m)

61 Example – Proton synchrotron (30GeV) at J-PARC

62 LHC at CERN (7TeV)

63 LHC Operation Log

CERN 64 Synchrotrons, Store rings, Colliding rings • Nearly all ring accelerators require some beam acceleration for – Actually increasing the beam energy and/or – Compensate for beam energy loss due to synchrotron radiation • Some ring accelerators are called “storage rings” as their mission is to hold the ring for a long period. • Some facility use a pair of ring accelerators to collide two opposing beams in an experimental hall – Colliding rings (colliders).

Energy Storage Colliding change in type? type? the rings? SuperKEKB No Yes Yes J-PARC MR Yes No No LHC MR Yes Yes Yes

65 Livingston Chart

By Stanley Livingston (1954)

Historical evolution of the beam energies.

66 Different presentation with more recent development.

67 S-band accelerator structure for use at KEK injector linac

This is a cut-away model for display.

68 Travelling Wave Accelerator Structure (2p/3)

CreatedCreated by: by Takuya Takuya Natsui Natsui, for KEK (KEK)open day display CreatedCreated by: by Takuya Takuya Natsui Natsui, for KEK (KEK)open day display Accelerator Resonant Cavity (Multi-cell Superconducting)

Niobium 9-cell cavity

If the time that it takes the beam particle to travel across one cell coincides with one half of the RF period, the particle will be continually accelerated, in case of a so-called p-mode standing-wave structure.

71 Acceleration with Resonant Cavities

• Single-cell “pillbox” cavity: by solving Maxwell’s equation one obtains –

• Where,

– c01 = 2.4048

– w010 = c01 c / b • This is called TM01 mode (fundamental mode, TM010 to be more exact) of a pillbox cavity.

K.Takata 72 Accelerator Subsystems – Acceleration Section

Particles Energy (Kinetic) Range Technique

Cockroft 0 up to 1 ~ a few MeV Ven de Graaf RF Qs < a few 100 MeV Drift-tube linac Ions / Protons low-b SC cavities linac (NC, SC) > a few 100 MeV Synchrotron < several 10 MeV Cyclotron

0 up to few hundred KeV Thermionic gun 0 up to a few MeV RF gun Electrons linac (NC, SC) > a few 100 MeV Synchrotron 73 RF Frequencies

• L band 1 - 2 GHz • S band 2 - 4 GHz • C band 4 - 8 GHz The naming of frequency ranges on • X band 8 - 12 GHz the left came apparently from the convention which was developed in • K band 12 - 40 GHz Rader-related research effort in • Q band 30 - 50 GHz Allied countries during WWII. • U band 40 - 60 GHz Other than that, no one seems to • V band 50 - 75 GHz know for sure why this pattern, • E band 60 - 90 GHz except perhaps L stands for LONG • W band 75 - 110GHz and S stands for SHORT. • F band 90 - 140 GHz • D band 110 - 170 GHz

74 Resonant Cavities • Quality factor (Q-value) of a cavity: – [stored energy in the cavity] / [energy loss over 1rad of RF oscillation] • In case of a TM01 mode, the stored energy in a pillbox cavity is 1 1 1 U = e E 2dV = e E 2VJ 2 (c ) ~ e E 2V ´0.25 2 0 ò 2 0 0 1 01 2 0 0

• Surface current in the cavity is

1 1 iwt 1 E0 æw ö iwt J = Bq = B(r)e = J1ç r÷e µ0 µ0 µ0 c è c ø

2 • Ohmic energy loss is surface integral of rsJ /2 - 2 b 1 æ E0 ö é 2 æ wr ö 2 æ wb öù DP = rs ç ÷ 2×2p J1 ç ÷rdr + 2pbdJ1 ç ÷ ç ÷ ê ò0 ú 2 è µ0c ø ë è c ø è d øû 2 1 E0 é b ù 2 = rs 2 2pbd ê1+ 2 úJ1 (c01) 75 2 Z0 ë c01 d û Resonant Cavities • From the previous page, the Q value that we seek is given by

w c µ c Q = U = 01 0 DP æ b ö 2r ç1+ ÷ s ç 2 2 ÷ è c01 d ø

• In case of copper Q ~ 5000, in case of superconducting Nb Q ~ 1010

76 Resonant Cavities

• Shunt impedance Rs of an accelerator cavity is defined as

2 Rs = (Energy gain V0 by a particle across the cavity) / DP

• For a pillbox cavity the Rs is given by

Z 2 d 1 R = 0 T 2 s pr b æ b 1 ö s ç1+ ÷J 2 (c ) 2 ç 2 ÷ 1 01 Rs V0 è c01 d ø = Q wU d / 2 æ wz ö E0 cosç ÷dz ò0 è v ø æ wd ö æ wd ö Geometric quantity of a cavity. T = = sinç ÷ /ç ÷ d E è 2v ø è 2v ø 0 2 • Where “T” is the transient factor.

• In case of copper: Rs = 15-50MW/m for 200MHz, 100MW/m for 3GHz 77 Superconducting Cavity at superKEKB

78 Accelerator Resonant Cavity (Single-cell superconducting)

This is an example of a single-cell super-conducting cavity which was used at KEKB. 79 Accelerator Cavities / Structures

• Q2: If fRF = 1.3GHz for a p-mode cavity, what should be the cell length? • A2: f = 1.3E9 Hz; c = 2.9979E8 m/s ! l = c/f = 0.23 m; p-mode cell length = l/2 = 0.12 m

• Q3: If fRF = 2.856GHz for a 2p/3-mode structure, what should be the cell length? • A3: f = 2.856E9 Hz; c = 2.9979E8 m/s ! l = c/f = 0.105 m;

2p/3-mode cell length = (2/3)l/2 = 0.035m

80 Accelerator Cavity / Structure - Comments • Cavities have many resonant modes. TM01 is the lowest and is most often used for beam acceleration. But, – Higher-order modes, such as TE11, also can be excited with an external RF source, – Or by the beam that traverses through them off axis,

– And do some harms. This may not be big problems for TE11 mode (~1.5 x TM01) many applications, but it is for some.

T.Higo, et al 81 Accelerator Resonant Cavity (Single-cell normal conducting)

T.Abe This is an example of a single-cell normal conducting cavity (which is used at superKEKB. It has “slots” for removing (damping) HOM, as excited by the beam, which are harmful for multi-bunch beam operation, and an energy storage cavity to reduce the effects of beam loading on the system. 82 Accelerator Cavity / Structure - Comments • Design, engineering and operation of accelerator cavities / structures is a huge area. – Exact evaluation of resonant frequencies, shunt impedance and quality factor have to be made through numerical calculations (still, an intuitive understanding important).

– Size variation ! variation of resonance frequencies ! mechanical tolerance and tuning issues. Similarly, temperature stabilization issues. (Q: if DT = 5deg, how much energy shift for an X-band structure?)

– “Couplers” to let the external RF power into the cavities and vice versa.

– In pulsed mode operation, the accelerator cavities exhibit transient behaviors at the beginning and end of RF pulses.

– Even in continuous wave operation, the accelerator

E.Kako, S.Noguchi et al cavities see transient effects when the beams pass83 through them. Microwave (RF) Source (Klystrons) velocity !

• For brevity, the solenoid beam focusing magnet is omitted from the illustration above. • Klystron, in a way, is a reversed accelerator, which extracts RF power from the beam. Velocity modulation • Klystrons, depending on the type, modulation Intensity operate in pulsed- or continual modes. All particles same speed speed same particles All repeat cavity; a via modulation 84 Microwave (RF) Source (Klystrons)

85 J-PARC Microwave (RF) Source (Modulator + Klystrons)

rModulator

T.Okugi

Klystrons for pulsed operation 86 A typical electron linac

Klystron DC PS Modulator Control equip/

Surface level (Klystron Gallery)

Waveguides Underground tunnel

Beam focusing Accelerator structures magnets (2m x 4)

87 Microwave (RF) Source (Modulator + Klystrons)

88 Tsukuba injector linac 89 Microwave RF Source (Klystrons) - Comments • As said in the previous page, klystrons are like small-scale reversed accelerator, and are more difficult ones at that.

– Relatively low beam energy (up to few hundred kV). – High current (tens of A) – So large beam power, and large space-charge effect. – Large beam size. – Opportunities for a good number of resonant behaviors, besides the RF power that you intend to produce.

• Design, engineering and operation of klystrons is a huge area, too, in a way similar to those for accelerator cavities / structures. – RF calculations and simulations, under prominent effect of space-charge force. – Tolerance and tuning issues. – RF windows to isolate the klystron vacuum and outside vacuum. Sometimes a cause of trouble ! another large area of studies which I cannot detail. – Cathode lifetime. Klystrons are a consumable component. Significantly more so than accelerator cavities / structures. 90 Beam Monitors

• Strip-line Type Beam Position • Generally, Monitors (BPM): with 4 x = k (S – S ) / (S + S ) electrodes, for use at ATF linac L R L R and extraction beamlines. y = k (SU – SD) / (SU + SD)

H.Hayano et al Monitoring of beam orbit • Data from many beam position monitors plotted along the direction of beam motion.

Bunch charge

~ 600m Beam Monitors

• Cavity Type Beam Position Monitors (BPM): Rather than seeing induced charges on electrodes, measure the transverse modes (TE-modes) that are induced by the beam when it passes off center of a cavity.

KEK-Pohan-SLAC Collaboration Beam Monitors

• Beam Current Monitors: BPMs can also measure the beam intensity but for better precision a dedicated beam current monitor is used, as shown on the right.

• Beam Profile Monitors with phospho-screens: – Direct measurement of the beam, in case of linac or beamlines.

– Measurement of synchrotron radiation light in case of rings (on the right). Beam Monitors • Beam Profile Measurement with interference method of SR light in rings. – Take advantage of the interference of SR light which comes through a slit pair. – Overcomes the diffraction limit in standard SR measurement.

a = beam size; g = “visibility” (clearness) l = wavelength; D = slit separation

L0 = distance from the light emission point

T.Mitsuhashi and T.Naito Beam Monitors • Beam Profile Measurement with Wire Scanners in the linac or in the beamlines. – Step the wire (or step the beam orbit) whose radius is assumed smaller than the beam size. – Look at the signal, whose strength would be proportional to the intercepted beam. – Profile the signal strength as function of the “stepping”. – Fundamentally a multi-pulse operation. Subject to limitation due to wire breakage.

H.Hayano et al Beam Monitors

• Beam size monitor with Compton scattering off interfering pattern of laser photon population.

• Data on left (2010/5) at ATF2: – Laser WL: 532 nm – Laser crossing: 3 deg – Fringe pitch: 3.81 µm – Modulation: 0.87 – Beam size: 310 +/- 30 nm

T.Tauchi Accelerator Subsystems – Beam Instrumentation

98 Controls

• Controls systems at particle accelerators must allow you to – Monitor – Analyze – Compute / Simulate – Control – Log • A wide range of synchronous and asynchronous signal processing / transmission must be managed. • Nearly a unique hotline to Schematic diagram of KEKB control system (N.Yamamoto) speak to the hardware, once the tunnel is closed for operation. Controls

KEK Conventional Facilities

• Sometimes the tunnel length becomes too big to stay inside a lab campus. – Going underground. – Going off site. – Safety issues.

• At any rate, you have to – Fit all required beamline components in wherever they have to go. – Connect them all either electronically, mechanically and vacuum-wise. – Allow enough space for installation and maintenance activities, plus, survey LHC from satellite and alignment sighting. – Bring in fresh air and provide adequate cooling (taking the heat the out). – Ensure safety for personnel and equipment.

EuroXFEL in Hamburg Conventional Facilities

f5200 mm

645 mm

EuroXFEL in Hamburg Things that Beams would Do Players Interaction via Effect

Q.E Thermal electrons / Photo-emission / Ionization

Material "!Beam Pair creation / Electro-magnetic shower EM / QED Absorption Elastic / Inelastic scattering

Static E-Field Acceleration / Deceleration / Bending Environment ! Beam Static B-Field Bending / Spin rotation RF Field Acceleration / Deceleration / Bending

Fundamental mode RF / High-order mode RF Beam ! Environment Transient Field Heating Synchrotron Light emission Beam "! Light Radiation Damping Compton Scattering QED Phenomena Space-charge forces Within a single bunch Beam "! Beam Beam-beam effects When two bunches cross each other

Physics Beam collision you look for Longitudinal EM Bunching / Debunching Beam ! Env. ! Beam Trasverse EM Emittance growth / instabilities / beam break-up

Accelerator is a device which overcomes, or takes advantages of these 106 phenomena, to let the beam do what you like it to do. Accelerator Subsystems – Typical Beam Manipulation

107 Accelerators – Differences and Similarities • You saw that accelerators vary widely in their organization, in accordance with their application, optimization, beam particles and size, but they also share similarities.

– Differences of accelerators come from • differences of what you like to do with/to the beam. – Similarities of accelerators come from • common nature of particle beams that you deal with.

• Learning particle accelerators means for us to learn,

– To identify what you like to do with the beam and – Find adequate technical solutions if they already exist and adopt them appropriately, or – Develop new technical solutions if they do not exist. – Now you have seen some such techniques. 108 Comments • Particle accelerators

– Consist of a number of subsystems for specific beam manipulation; – Use many components that do specific things with the beam. – Particle accelerators are a complex, almost organic system.

• Performance of particle accelerators

– Is determined by the performance of accelerator subsystems, – Whose performance is determined by that of individual components, – And the systems design which puts them together.

• Beam

– Is the object that you try to control and tame, but – The beam is also a friend who tells you what and how you are doing right or wrong. – Be prepared to work with the beam.

109 Conclusions

• We tried a very coarse, quick walk-through of subsystems of particle accelerators.

• If you wish to become expert on anything, all the subject matters introduced here must be more systematically and seriously re- surveyed.

• You have to read some textbooks (examples mentioned earlier), come to subsequent lectures in this course, solve problems on your own and so on.

• My sincere thanks go to Drs. K.Takata, T.Okugi, E. Kako, H. Hayano, J.Urakawa, M.Poole and many others, whose work I am freely taking advantage of, to create this note.

110