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Accelerate This!

Accelerate This!. Using the forces of electricity and magnetism to make tiny things go really fast Daniel Friedman, St. John’s School. Accelerating a charged particle. Remember ‘opposites attract’ and ‘likes repel’?. Let’s call it Coulomb’s Law!. Accelerating a charged particle.

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Accelerate This!

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  1. Accelerate This! Using the forces of electricity and magnetism to make tiny things go really fast Daniel Friedman, St. John’s School

  2. Accelerating a charged particle Remember ‘opposites attract’ and ‘likes repel’? Let’s call it Coulomb’s Law!

  3. Accelerating a charged particle The force on charged particle q is due to the charge Q of another nearby particle; For two charges of the samesign:

  4. Another way to look at this uses the idea of an electric field If we only know one of the charges (Q), we can still calculate the force per unit of charge some unknown q would ‘feel’:

  5. Still another way:Voltage = work/unit charge To move a charge in the presence of a repulsive Coulomb force, we have to do some work. But we can express this in terms of the E field:

  6. Voltage is sometimes called ‘electromotive force’ but it is better described in terms of energy We also use the term ‘potential difference’ as a synonym for voltage.

  7. A charge crossing through a potential difference gains kinetic energy The energy measure of particle physics is the electron volt (eV), defined as the energy of a single electron across a potential difference of 1 Volt: DKE = qV

  8. An eV is tiny! 1 eV = 1.6x10-19 Joule keV = 103 MeV = 106GeV = 109 TeV = 1012 Kilo – Mega – Giga – Terra A billion eV was also known as BeV, which led to the term ‘Bevatron’.

  9. Want high energy?You’ll need a lot of batteries If you put 600 billion D cell batteries in series, end to end, you’d get 900 billion volts – and each electron would have 900 GeV! But your circuit would be 23 million miles long!

  10. Some typical energies keV=103 MeV=106 GeV=109 TeV=1012 Visible light photon: 1.5-3.5 eV Ionize atomic hydrogen (free the proton!): 13.6 eV Your TV set: 20 keV Medical X-Rays: 200 keV Natural radioactivity (a+2, b-, g): 2-5 MeV

  11. Some unusual energies FermiLab Tevatron: 900 GeV CERN’s LHC (under construction): 7 TeV A Roger Clemens fastball: 7 x108 TeV (but that’s spread over a lot of particles!) Highest energy cosmic ray showers: 109 GeV (106 TeV)

  12. Natural Radioactivity Ernest Rutherford used naturally occurring alpha particles with energies of approximately 5 MeV to discover the nucleus.

  13. At this energy level, all Rutherford could detect were the collisions between ‘solid’ objects

  14. But to see inside the nucleus, we need higher energy!

  15. Welcome to Big Science: FermiLab main accelerator ring over 4 miles around; 900 GeV

  16. Particle accelerators! SLAC is 3 km long. Initially 18-20 GeV; upgraded to 50 GeV

  17. Early Accelerators Using a very high DC voltage (large E field) to accelerate an electron across a small gap.

  18. Cockroft-Walton Accelerators John Cockroft and Ernest Walton, students of Rutherford at Cambridge, were leaders in developing this technology.

  19. CW accelerators produce very high DC voltages across a small ‘gap’

  20. The high voltage is obtained by means of a ‘diode-capacitor ladder’

  21. Popular science fiction liked the look of these early accelerators

  22. Robert Van deGraaf uses a moving belt to build charge by friction

  23. 1931: A giant Van deGraaf in an old dirigible hanger Each sphere was at a potential of 750 kV for a total potential difference of 1.5 MV! The observation labs were inside the spheres!

  24. Question: Why can the observer sit inside the sphere without harm?

  25. A big enough Van de Graaf can produce 10 MeV: the radius of the sphere is the voltage limit

  26. e- Linear Accelerators + - Copper rings are used as the accelerating field plates.

  27. e- Linear Accelerators - The field polarity is switched by a radio frequency oscillator. Acceleration occurs due to the E field across each gap: F = Eq = ma +

  28. e- Linear Accelerators The field polarity is switched by a radio frequency oscillator. Acceleration occurs due to the E field across each gap: F = Eq = ma - +

  29. e- Linear Accelerators The disks act as ‘collimators,’ blocking any electrons that are not going in the direction of the beam. Interactive linac

  30. The biggest linacs use of many thousands of gaps and generate 100’s of MeV – requiring a very straight hole in the ground!

  31. Some medical devices are small linear accelerators You might see one the next time you go to the dentist!

  32. Linacs deliver ‘bunches’ of electrons Very high-grade vacuum:Internal pressure 10-12 torr! (1 atm=760 torr)

  33. Let’s introduce the magnetic force A charged particle with velocity v in the presence of an external magnetic field of strength B experiences a forceif the mag field has a component that is perpendicular to the motion of the charge. Sine=opposite/hypoteneuse B q v

  34. The magnetic force is perpendicular to the velocity of the charge A perpendicular force can only change the direction of motion, not the speed.If the external B field is constant, the particle moves in a circle.

  35. The magnetic force is given by Known as the ‘cross product’.

  36. The direction of the magnetic force is given by the ‘right hand rule’ Fingers along the B field, thumb in the direction of motion of a positive charge, palm points in the direction of the force.

  37. Putting these forces together, the ‘Lorentz force.’ It is vital to note that E and B are always perpendicular.

  38. Cyclotrons: External B field creates a spiral path Relatively low potential difference across the gap between opposing ‘D’ ’s. Acceleration each time gap is crossed.

  39. Top view, showing one of the ‘D’ electrode cavities

  40. Cyclotrons: particles accelerate around a spiral path As particles gain energy, they spiral out.

  41. Cyclotron Resonance Radius increases with increasing speed; but the time required to complete ½ circle remains constant. The frequency of the E field may therefore be kept constant.

  42. Cyclotrons First cyclotron 4 inches in diameter 80 keV 1MeV Lawrence Cyclotron (1932) 11 inches in diameter

  43. Cyclotrons President Eisenhower inspects Columbia’s 400 MeV Cyclotron (1950)

  44. Cyclotrons Modern 250 MeV Cyclotron might be part of a PET scan device or cancer treatment facility

  45. Cyclotrons: problem 1 Higher energy requires more turns around the ring. This means a bigger ring – and a bigger, more expensive magnet.

  46. Cyclotrons: problem 2 Iron core magnets can withstand a maximum of about 2 Tesla before the iron starts to turn purple (and burn up). The maximum B field strength thus limits the energy at the outside edge.

  47. The Synchrotron: particle racetracks! Smaller magnets are used only to steer and focus the particles.Changing the B field strength to compensate for increasing velocity maintains a fixed radius.

  48. Synchrotrons Pushing the particle at just the right time increases speed – just like pushing a child on a swing.

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