Accelerator Physics Alex Bogacz Jefferson Lab bogaczjlab org

Accelerator Physics Alex Bogacz (Jefferson Lab) / bogacz@jlab. org Geoff Krafft (Jefferson Lab/ODU) / krafft@jlab. org and Subashini De Silva (ODU) / sdesilva@jlab. org Randika Gamage (ODU) / bgama 002@odu. edu Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Physics Lecture Accelerator 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 1

Introductions and Outline Syllabus Week 1 Week 2 Introduction Course logistics, Homework, Exams: http: //casa. jlab. org/publications/USPAS_Summer_2016. shtml Relativistic mechanics review Relativistic E&M review, Cyclotrons Survey of accelerators and accelerator concepts Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Physics Lecture Accelerator 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 2

Syllabus – week 1 Mon 13 June 0900 -1200 Lecture 1 ‘Relativity, EM Forces - Historical Introduction Mon 13 June 1330 -1630 Lecture 2 ‘Weak focusing and Transverse Stability’ Tue 14 June 0900 -1200 Lecture 3 ‘Linear Optics’ Tue 14 June 1330 -1630 Lecture 4 ‘Phase Stability, Synchrotron Motion’ Wed 15 June 0900 -1200 Lecture 5 ‘Magnetic Multipoles, Magnet Design’ Wed 15 June 1330 -1630 Lecture 6 ‘Particle Acceleration’ Thu 16 June 0900 -1200 Lecture 7 ‘Coupled Betatron Motion I’ Thu 16 June 1330 -1630 Lecture 8 ‘Synchrotron Radiation’ Fri 17 June 0900 -1200 Lecture 9 ‘Coupled Betatron Motion II’ Thomas Jefferson National Accelerator Fri 14 June 1330 -1630 Recitations & Mid Term Facility Exam Operated by JSA for the U. S. Department of Energy Physics Lecture Accelerator 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 3

Syllabus – week 2 Mon 20 June 0900 -1200 Lecture 10 ‘Fundamentals of RF Cavities’ Mon 20 June 1330 -1630 Lecture 11 ‘Radiation Distributions’ Tue 21 June 0900 -1200 Lecture 12 ‘Beam Dynamics of Energy Recovery Linacs’ Tue 21 June 1330 -1630 Lecture 13 ‘X-ray Sources/ FELs’ Wed 22 June 0900 -1200 Lecture 14 ‘Radiation Damping’ Wed 22 June 1330 -1630 Lecture 15 ‘Statistical Effects I’ Thu 23 June 0900 -1200 Lecture 16 ‘Low Emittance Lattices’ Thu 23 June 1330 -1630 Lecture 17 ‘Statistical Effects II’ Fri 24 June 0900 -1300 Final Exam Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Physics Lecture Accelerator 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 4

Homework and Schedule Homework is way more than 1/3 of your grade (40%) Suba and Randy are grading Collected at start of every morning class TAs will get it back to you the next day Lectures will run 09: 00 -12: 00, 13: 30 -16: 30 Exams: Mid Term (20%) Final (40%) Mid-term (Friday, June 14) Final (Friday, June 21) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Physics Lecture Accelerator 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 5

Relativity, EM Forces: Historical Introduction S. A. Bogacz, G. A. Krafft, S. De. Silva and R. Gamage Jefferson Lab and Old Dominion University Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 6

Relativity Review Accelerators: applied special relativity Relativistic parameters: Later b and g will also be used for other quantities, but the context should usually make them clear g = 1 (classical mechanics) to ~ 2. 05 x 105 (to date, LEP) Total energy U, momentum p, and kinetic energy W Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 7

Convenient Units How much is a Te. V? Energy to raise 1 g about 16 mm against gravity Energy to power 100 W light bulb 1. 6 ns But many accelerators have 1010 -12 particles Single bunch “instantaneous power” of tens of Terawatts Highest energy cosmic ray ~300 Ee. V (3 x 1020 e. V or 3 x 108 Te. V!) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 8

Relativity Review (Again) Accelerators: applied special relativity Relativistic parameters: Later b and g will also be used for other quantities, but the context should usually make them clear g = 1 (classical mechanics) to ~ 2. 05 x 105 Total energy U, momentum p, and kinetic energy W Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 9

Convenient Relativity Relations All derived in the text, hold for all g In “ultra” relativistic limit b ≈ 1 Usually must be careful below g ≈ 5 or U ≈ 5 mc 2 Many accelerator physics phenomena scale with gk or (bg)k Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 10

Frames and Lorentz Transformations The lab frame will dominate most of our discussions But not always (synchrotron radiation, space charge…) Invariance of space-time interval (Minkowski) Lorentz transformation of four-vectors For example, time/space coordinates in z velocity boost Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 11

Four-Velocity and Four-Momentum The proper time interval dt=dt/g is Lorentz invariant So we can make a velocity 4 -vector We can also make a 4 -momentum Double-check that Minkowski norms are invariant Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 12

Mandelstam Variables Lorentz-invariant two-body kinematic variables p 1 -4 are four-momenta √s is the total available center of mass energy Often quoted for colliders Used in calculations of other two-body scattering processes Moller scattering (e-e), Compton scattering (e-g) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 13

Relativistic Newton Equation But now we can define a four-vector force in terms of fourmomenta and proper time: We are primarily concerned with electrodynamics so now we must make the classical electromagnetic Lorentz force obey Lorentz transformations Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 14

Relativistic Electromagnetism Classical electromagnetic potentials can be shown to combine to a four-potential (with c = 1): The field-strength tensor is related to the four-potential E/B fields Lorentz transform with factors of g, (bg) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 15

Lorentz Lie Group Generators Lorentz transformations can be described by a Lie group where a general Lorentz transformation is where L is 4 x 4, real, and traceless. With metric g, the matrix g. L is also antisymmetric, so L has the general six-parameter form Deep and profound connection to EM tensor Fab (see the Appendix) J. D. Jackson, Classical Electrodynamics 2 nd Ed, Section 11. 7 Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 16

Relativistic Electromagnetism II The relativistic electromagnetic force equation becomes Thankfully we can write this in somewhat simpler terms That is, “classical” E&M force equations hold if we treat the momentum as relativistic, If we dot in the velocity, we get energy transfer Unsurprisingly, we can only get energy changes from electric fields, not (conservative) magnetic fields Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 17

Constant Magnetic Field (E = 0) In a constant magnetic field, charged particles move in circular arcs of radius r with constant angular velocity w: For we then have Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 18

Rigidity: Bending Radius vs Momentum Accelerator (magnets, geometry) Beam This is such a useful expression in accelerator physics that it has its own name: rigidity Ratio of momentum to charge How hard (or easy) is a particle to deflect? Often expressed in [T-m] (easy to calculate B) Be careful when q≠e!! A very useful expression Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 19

Cyclotron Frequency Another very useful expression for particle angular frequency in a constant field: cyclotron frequency In the nonrelativistic approximation Revolution frequency is independent of radius or energy! Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 20

Lawrence and the Cyclotron Can we repeatedly spiral and accelerate particles through the same potential gap? Accelerating gap DF Ernest Orlando Lawrence Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 21

Cyclotron Frequency Again Recall that for a constant B field Radius/circumference of orbit scale with velocity Circulation time (and frequency) are independent of v Apply AC electric field in the gap at frequency frf Particles accelerate until they drop out of resonance Note a first appearance of “bunches”, not DC beam Works best with heavy particles (hadrons, not electrons) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 22

A Patentable Idea 1934 patent 1948384 Two accelerating gaps per turn! Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 23

All the Fundamentals of an Accelerator Large static magnetic fields for guiding (~1 T) ~13 cm But no vertical focusing HV RF electric fields for accelerating (No phase focusing) (Precise f control) p/H source, injection, extraction, vacuum 13 cm: 80 ke. V 28 cm: 1 Me. V 69 cm: ~5 Me. V … 223 cm: ~55 Me. V (Berkeley) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 24

Livingston, Lawrence, 27”/69 cm Cyclotron M. S. Livingston and E. O. Lawrence, 1934 Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 25

The Joy of Physics Describing the events of January 9, 1932, Livingston is quoted saying: “I recall the day when I had adjusted the oscillator to a new high frequency, and, with Lawrence looking over my shoulder, tuned the magnet through resonance. As the galvanometer spot swung across the scale, indicating that protons of 1 -Me. V energy were reaching the collector, Lawrence literally danced around the room with glee. The news quickly spread through the Berkeley laboratory, and we were busy all that day demonstrating million-volt protons to eager viewers. ” APS Physics History, Ernest Lawrence and M. Stanley Livingston Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 26

Modern Isochronous Cyclotrons Higher bending field at higher energies But also introduces vertical defocusing Use bending magnet “edge focusing” (Tuesday magnet lecture) 590 Me. V PSI Isochronous Cyclotron (1974) 250 Me. V PSI Isochronous Cyclotron (2004) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 27

Electrons, Magnetrons, ECRs Radar/microwave magnetron Cyclotrons aren’t good for accelerating electrons Very quickly relativistic! But narrow-band response has advantages and uses Magnetrons generate resonant high-power microwaves from circulating electron current ECRs generate high-intensity ion beams and plasmas by resonantly stripping electrons with microwaves ECR plasma/ion source Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 28

Cyclotrons Today Cyclotrons continue to evolve Many contemporary developments Superconducting cyclotrons Synchrocyclotrons (FM modulated RF) Isochronous/Alternating Vertical Focusing (AVF) FFAGs (Fixed Field Alternating Gradient) Versatile with many applications even below ~ 500 Me. V High power (>1 MW) neutron production Reliable (medical isotope production, ion radiotherapy) Power+reliability: ~5 MW p beam for ADSR (accelerator driven subcritical reactors, e. g. Thorium reactors) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 29

ACCEL Radiotherapy Cyclotron Bragg peak Distinct dose localization advantage for hadrons over X-rays Also present work on proton and carbon radiotherapy fast-cycling synchrotrons Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 30

Brief Survey of Accelerator Concepts Producing accelerating gaps and fields (DC/AC) Microtrons and their descendants Betatrons (and betatron motion) Synchrotrons Fixed Target Experiments Colliders and Luminosity (Livingston Plots) Light Sources (FELs, Compton Sources) Others include Medical Applications (radiotherapy, isotope production) Spallation Sources (SNS, ESS) Power Production (ADSR) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 31

DC Accelerating Gaps: Cockcroft-Walton Source Rectifiers Accelerates ions through successive electrostatic voltages First to get protons to >Me. V Continuous HV applied through intermediate electrodes Rectifier-multipliers (voltage dividers) Limited by HV sparking/breakdown FNAL still uses a 750 k. V C-W Target ~1930 1. 4 Me. V Cavendish Lab Also example of early ion source H gas ionized with HV current Provides high current DC beam Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 32

DC Accelerating Gaps: Van de Graaff How to increase voltage? R. J. Van de Graaff: charge transport Electrode (1) sprays HV charge onto insulated belt Carried up to spherical Faraday cage Removed by second electrode and distributed over sphere Limited by discharge breakdown ~2 MV in air Up to 20+ MV in SF 6! Ancestors of Pelletrons (chains)/Laddertrons (stripes) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 33

DC Accel Gaps: Tandem Van de Graaff Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 34

From Electrostatic to RF Acceleration Cockcroft-Waltons and Van de Graaffs have DC voltages, E fields What about putting on AC voltage? Attach consecutive electrodes to opposite polarities of ACV generator Electric fields between successive electrodes vary sinusoidally Consecutive electrodes are 180 degrees out of phase ( mode) Wideroe linac At the right drive frequency, particles are accelerated in each gap While polarity change occurs, particles are shielded in drift tubes To stay in phase with the RF, drift tube length or RF frequency must increase at higher energies Pagani and Mueller 2002 Operated by JSA for the U. S. Department of Energy Thomas Jefferson National Accelerator Facility Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 35

Resonant Linac Structures Wideroe linac: mode Alvarez linac: 2 mode Need to minimize excess RF power (heating) Make drift tubes/gaps resonant to RF frequency In 2 mode, currents in walls separating two subsequent cavities cancel; tubes are passive We’ll cover RF and longitudinal motion later this week… Wideroe linac Drift tube linac ALICE HI injector, IPN Orsay Saturne, Saclay Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro 36 USPAS, Fort Collins, CO, June 13 -24, 2016 36

Advanced Acceleration Methods How far do accelerating gradients go? Superconducting RF acceleration: ~40 MV/m CLIC: ~100 MV/m Two-beam accelerator: drive beam couples to main beam Dielectric wall acceleration: ~100 MV/m Induction accelerator, very high gradient insulators Dielectric wakefield acceleration: ~GV/m Laser plasma acceleration: ~30 GV/m electrons to 1 Ge. V in 3. 3 cm particles ride in wake of plasma charge separation wave Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 37

Cyclotrons (Again) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 38

Microtrons What about electrons? Microtrons are like cyclotrons but each revolution electrons “slip” by integer # of RF cycles Trades off large # of revs for minimal RF generation cost Bends must have large momentum aperture Used for medical applications today (20 Me. V, 1 big magnet) Mainz MAMI: 855 Me. V, used for nuclear physics Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 39

Recirculating Linacs and ERLs CEBAF Recirculating linacs have separate arcs, longer linacs CEBAF: 4 ->6 ->12 Ge. V polarized electrons, 2 SRF linacs Higher energy at cost of more linac, separated bends Energy recovery linacs recirculate exactly out of phase Raise energy efficiency of linac, less beam power to dump Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 40

Phase Stability M 1, 2: More energy, arrive earlier relative to P N 1, 2: Less energy, arrive later relative to P Consider a series of accelerating gaps (or a ring with one gap) By design there is a synchronous phase Fs that gains just enough energy to hit phase Fs in the next gap P 1, 2 are fixed points: they “ride the wave” exactly in phase If increased energy means increased velocity (“below transition”) M 1, N 1 will move towards P 1 (local stability) => phase stability M 2, N 2 will move away from P 2 (local instability) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 41

Phase Stability Implies Transverse Instability For phase stability, longitudinal electric field must have a negative gradient. But then (source-free) Maxwell says There must be some transverse defocusing/diverging force! Any accelerator with RF phase stability (longitudinal focusing) needs transverse focusing! (solenoids, quads…) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 42

LBL Bevatron Ed Mc. Millan and Ed Lofgren Last and largest weak-focusing proton synchrotron 1954, Beam aperture about 4’ square!, beam energy to 6. 2 Ge. V Discovered antiproton 1955, 1959 Nobel for Segre/Chamberlain (Became Bevelac, decommissioned 1993, demolished recently) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 43

Fixed Target Experiments Anti-proton production: Why did the Bevatron need 6. 2 Ge. V protons? Antiprotons are “only” 930 Me. V/c 2 (times 2…) Bevatron used Cu target, p + n ￫ p + n + pbar Mandelstam variables give: Fixed Target experiment c 2 Available CM energy scales with root of beam energy Main issue: forward momentum conservation steals energy Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 44

Two Serious Problems These machines were getting way too big Bevatron magnet was 10, 000 tons Apertures scale linearly with machine size, energy (Length/circumference scales linearly with energy at fixed field strength too…) Fixed target energy scaling is painful Available CM energy only scales with √Ebeam Accelerator size grew with the square of desired CM energy Something had to be done…. . Strong Focusing (1952) and Colliders (1958 -62) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 45

Alternating Gradient Synchrotron (AGS) First strong-focusing proton synchrotron Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 46

Collider Experiments What if the Bevatron was a collider? Antiprotons are “only” 930 Me. V/c 2 (times 2…) Two-body system (Mandelstam variables) gives (again): Collider’s case Linear scaling with beam energy! Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 47

First Electron Collider Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 48

Tevatron/Main Injector Fermilab Tevatron: First Te. V-scale accelerator; Large Superconducting Bends Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 49

Large Hadron Collider (former LEP tunnel) The Large Hadron Collider (LHC) is the world's largest and most powerful particle collider ever built, and the largest single machine in the world. It was built CERN between 1998 and 2008. It lies in a tunnel 27 kilometres in circumference, as deep as 175 metres. On May 20 2015, the LHC reached center of mass energy of 13 Te. V (the current world record). Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 50

ILC - Energy Frontier Lepton Collider The International Linear Collider (ILC) is a proposed particle accelerator that would be built in a 31 km long underground tunnel. It would collide electrons and positrons head on in the middle of the tunnel reaching multi-Te. V center of mass energies. Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 51

Luminosity L is a measure of how many interactions of cross section s can be created per unit time Lint is integrated luminosity, an important factor of production for colliders [L] = cm-2 s-1, [Lint] = cm-2 (1 ba=10 -24 cm; 1 pb-1=1036 cm-2) For equal-sized head-on Gaussian beams in a collider sx, y are rms beam sizes, h is number of bunches Colliding 100 mm 7. 5× 109 p bunches at 100 k. Hz for 1 year gives about 1 pb-1 of integrated luminosity Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 52

Evolution of RHIC Collider Luminosities W. Fischer, http: //www. rhichome. bnl. gov/RHIC/Runs Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 53

Evolution of Hadron Collider Luminosities W. Fischer, http: //www. rhichome. bnl. gov/RHIC/Runs Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 54

Livingston Plots Livingston observed that accelerator energy was growing exponentially (in 1950) Still holds true over 60 years (!) later Technologies tend to saturate then new technologies are introduced (G. Hoffstaetter, Cornell) Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 55

Appendix: Lorentz Lie Group Generators Lorentz transformations can be described by a Lie group where a general Lorentz transformation is where L is 4 x 4, real, and traceless. With metric g, the matrix g. L is also antisymmetric, so L has the general six-parameter form Deep and profound connection to EM tensor Fab J. D. Jackson, Classical Electrodynamics 2 nd Ed, Section 11. 7 Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 56

Appendix: Lorentz Lie Group Generators A reasonable basis is provided by six generators Three generate rotations in three dimensions Three generate boosts in three dimensions Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 57

Appendix: Lorentz Lie Group Generators and are diagonal. and for any unit 3 -vector Nice commutation relations: We can then write the Lorentz transformation in terms of two three-vectors (6 parameters) as Electric fields correspond to boosts Magnetic fields correspond to rotations Deep beauty in Poincare, Lorentz, Einstein connections Thomas Jefferson National Accelerator Facility Operated by JSA for the U. S. Department of Energy Lecture 1 - Relativity, EM Forces, Intro USPAS, Fort Collins, CO, June 13 -24, 2016 58