Physics 736. Experimental Methods in Nuclear-, Particle-, and Astrophysics. - Accelerator Techniques: Introduction and History -

Transcription

1 Physics 736 Experimental Methods in Nuclear-, Particle-, and Astrophysics - Accelerator Techniques: Introduction and History - Karsten Heeger heeger@wisc.edu

2 Homework #8 Karsten Heeger, Univ. of Wisconsin NUSS, July 13, 2009

3 Question 1

4 Question 1 Mathematica

5 Question 2 maybe show axes from 0 to 5

6 Question 3 linear plots should show exponential. log plots should look linear

7 Question 3 graphs should have enough resolution to see differences between MC and function

8 Question 4 you may want to plot this on logscale to show difference between function and MC

9 Question 4 how to do it: 1. either use inverse of distribution function, or 2. use acceptance-rejection method

10 Question 5 correlation coefficient=0

11 Question 5 analytical variance

12 Question 5 analytical variance for distribution rotated 30 degrees correlation coefficient=0.85 var(f) = 282

13 Question 5 MC data

14 Question 6

15 Question 6

16 Question 6 likelihood function

17 Question 6 PDF for measured times PDF for simulated data

18 Question 6 simulated data and PDF for measured times x 100

19 Question 6 1-D fit 2-D fit

20 Topics accelerators: introduction history tools of particle and nuclear physics

21 II Karsten Heeger, Univ. of Wisconsin NUSS, July 13, 2009

22 History of Accelerators energy growth of accelerators and storage rings energy increase by factor of 10 every 7 years historically, new technology has appeared whenever previous technology reached saturation e + e - machines typically match hadron machines with x10 nominal energy

23 Roads to Discovery high energy probe smaller scales produce new particles

24 Roads to Discovery high energy probe smaller scales produce new particles high luminosity detect the presence of rare processes precision measurements of fundamental parameters

25 Cross Section n Area of target Hard Sphere - n Measured in barns = cm 2 1 mbarn = 1 fm 2 - size of proton n Cross-section depends upon process e + e W + W e + e e + e σ = πr 2 about 16 pb (others fb or less) technically infinite (E field)

26 Luminosity n Intensity or brightness of an accelerator n Events Seen = Luminosity x cross-section Rare processes (fb) need lots of luminosity (fb -1 ) n In a storage ring N = L σ L = 1 f u N 1 N 2 4π σ x σ y Current Spot size More particles through a smaller area means more collisions

27 Luminosity Imagine a blue particle colliding with a beam of cross section area - A Probability of collision is For N particles in both beams Suppose they meet f times per second at the revolution frequency Event rate Make big LUMINOSITY Make small

28 Types of Accelerators n n Linear Accelerator (one-pass) Storage Ring (multi-turn) n n Fixed Target (one beam into target) Collider (two beams colliding) n electrons (e + e - ) n protons (pp or pp)

29 Types of Accelerators n Static Accelerators n Cockroft-Walton n Van-de Graaff n Linear n Cyclotron n Synchrotron n Storage Ring

30 Circular or Linear Accelerators n Linear Accelerator u Electrostatic u RF linac n Circular Accelerator u Cyclotron u Synchrotron u Storage Ring

31 Beamline Elements Dipole (bend) magnets Quadrupole (focusing) magnets Also Sextupoles and beyond

32 Motion in Electric and Magnetic fields For single particle, with no radiation losses and no space charge effects: There are many possibilities, depending on existence and timedependence of For example, if there is no magnetic field and a time-independent electric field along the z-axis, then electrostatic accelerator. If the electric field is time-dependent, then Linac.

33 Motion in Electric and Magnetic fields Accelerator w B r Cyclotron Fixed Fixed Variable Synchrocyclotron Variable Fixed Variable Synchrotron Variable Variable Fixed

34 Motion in Electric and Magnetic fields Cyclotrons: constant frequency orbital accelerator, but one in which the orbit radius increases

35 Motion in Electric and Magnetic fields as mass/energy increases, orbital frequency changes and resonance condition of cyclotron is no longer fulfilled Syncrocyclotrons: modulate the frequency sector focused cyclotron: split magnet into segments, abandon cylindrical symmetry of B

36 Motion in Electric and Magnetic fields Synchrotrons: Injector ii ti \\. ^taa.- n'' - t chamber (donut) Deflection magnet Focusing magnets (quadrapole doublets constant radius accelerator where both the frequency and the magnetic field vary with time in order to maintain the synchronism condition. angular frequency increases at B-dependent rate, initially fast but then more and more slowly

37 Synchrotron Use smaller magnets in a ring + accelerating station 3 GeV protons BNL 1950s Basis of all circular machines built since Fixed-target mode severely limiting energy reach synchrotrons are now the main machine of high-energy physics

38 Storage Rings Two beams counter-circulating in same beam-pipe Collisions occur at specially designed Interaction Points RF station to replenish synchrotron losses

39 Beam Transport and Delivery Emittance must be as small as possible and the density of points in phase space ( brightness ) as high as possible. Key concept is that of emittance : each particle of the beam can be represented by a single point in the 6-dimensional phase space (x, y, z, p x, p y, p z ). Volume occupied by these points is the 6-D emittance of the beam.

40 Liouville Theorem In the absence of collisions or dissipative processes, the local density in phase space remains constant. Alternatively: For a system of non-interacting particles that are in a conservative system, the density in phase space along the trajectory is invariant. There are a number of apparent violations of Liouville s theorem, most of them leading to an increase of the beam emittance, e.g. 1. Space charge forces between beam particles increase emittance. 2. Beam-beam and beam-gas scattering do the same. 3. Foil stripping of H - ions into H +, at the point of injection into a synchrotron, also increases emittance. 4. Synchrotron radiation (see later) can lead to a reduction in phase-space volume ( damping ).

41 Types of Accelerators n n Linear Accelerator (one-pass) Storage Ring (multi-turn) n n Fixed Target (one beam into target) Collider (two beams colliding) n electrons (e + e - ) n protons (pp or pp)

42 Fixed Target Experiments SLAC endstation A GeV electrons

43 Colliding Beams DESY HERA 1990s

44 Center of Mass Energy To produce a particle, you need enough energy to reach its rest mass. Usually, particles are produced in pairs from a neutral object. To produce e + e tt requires 2x175 GeV = 350 GeV of CM Energy E 2 CM = m m E 1 E 2 2 p 1 p 2 Head-on collisions: One electron at rest: E 2 CM =2E 1 E 2 2 p 1 p 2 =4E 2 E 2 CM =2E 1 E 2 =2E 1 m 2 Need 30,000,000 GeV electron...

45 Future of Fixed Target Experiments - neutrino factory will be based on an intense p beam impinging on fixed target, capture of pions and then of muons, and then acceleration of the latter. - Similar problems for the design of neutron spallation sources and of radioactive beam facilities. n Fixed-target still useful for secondary beams NuTeV Neutrino Production

46 Largest HEP Accelerator Labs

47 Fermilab Tevatron Highest Energy pp collider: 1.96 TeV top quark, Higgs search, new physics

48 SLAC - SLC and PEPII SLAC Linear Collider ( ) Z-pole, EW physics, B-physics, polarized beams PEPII Asymmetric Storage Ring (1999-present) 3 GeV e + on 9 GeV e - Very high luminosity, CP Violation, B-physics, rare decays

49 Large Hadron Collider at CERN Under construction in old LEP tunnel Will collide pp at 14 TeV (mini-ssc) Higgs, EW symmetry breaking, new physics up to 1 TeV

50 Large Hadron Collider at CERN

51 Types of Accelerators n n Linear Accelerator (one-pass) Storage Ring (multi-turn) n n Fixed Target (one beam into target) Collider (two beams colliding) n electrons (e + e - ) n protons (pp or pp)

52 Physics of Electron vs Proton Colliders n n P s Can win by accelerating protons ( mp m e ) 2 = E4 m 2 0 R2 ( 938MeV 0.511MeV ) 2 = But protons aren t fundamental Only small fraction at highest energy Don t know energy (or type) of colliding particles

53 Physics of Electron vs Proton Colliders When we collide protons we collide complex assemblies of three quarks Only two quarks interact Their available energy is on average only 10% of the total centre of mass energy We do not know which quarks they are Hence in some ways 100 GeV LEP is as good as 1000 GeV TEVATRON

54 Large Hadron Collider Proposed 1 TeV e + e - collider Similar energy reach as LHC, higher precision

55 International Linear Collider Particle Type: e + e - Energy CM: 500 GeV (800 GeV) Luminosity: First Beams: (?) Will allow detailed measurements of LHC finds. Needs to be linear since circular machine needs about 50 times the input power of LEP (for same diameter)!

56 International Linear Collider is the challenge High gradient cavities to keep length short Sophisticated damping rings to reduce emittance Unprecedented instrumentation and survey Controls/safety to deal with 2MW stored beam energy Need for new ideas on acceleration, which means both high field gradients and high phase space density.

57 Plasma Wave Acceleration A laser pulse traveling through a plasma, indicated by the ellipse at right, accelerates bunches of free electrons (center) in its wake. Recent results are promising, with 14GeV over a distance of 30cm The question of emittance preservation is still open See recent review article in Physics World, Feb. 2006

58 Table taken from W. Scarf & W. Wiesczycka, Proc. EPAC2000 CATEGORY NUMBER Ion implanters 7000 Industry 1500 non-nuclear research 1000 Radiotherapy 5000 Medical isotopes 200 Hadron therapy 20 SR sources 70 Nuclear & Particle physics res. 110 TOTAL Accelerators for particle and nuclear physics are a small fraction of the total.