Introduction to particle accelerators and their applications - Part I: how they work

Transcription

1 Introduction to particle accelerators and their applications - Part I: how they work Gabriele Chiodini Istituto Nazionale di Fisica Nucleare Sezione di Lecce PhD lessons in Physics for Università del Salento (20 hours, 4 CFD) 1

2 Introduction You are new in the field of accelerators Only basic concepts are going to be introduced Completely intuitive approach Clarify the concepts of physics, no mathematics, no rigorous scientific derivation 2 /49 G. Chiodini - May 2015

3 What is an accelerator In the first half of the '900 accelerating structures are built to increase the kinetic energy of charged atoms ( ions ) and induce new nuclear reactions by collision with a target ( artificial radioisotopes ). Applied Physics In the second half of the 900 accelerator complex are built to reach energies higher and higher ( ultrarelativistic energy) and study the infinitesimal properties of the matter ( subatomic particles and fundamental interactions ). Fundamental Physics 3 /49 G. Chiodini - May 2015

4 How a particle is accelerated Classic mechanics (Newton) Force = mass x acceleration: F=ma (It is false for speed near the speed of light) momentum = mass x velocity: p=mv Relativistic mechanics (Einstein) increase of p = force x time: Δp=FT (always true) p=mv: where m is the relativistic mass Δp=pfinal-pinitial ~ mδv + Δmv: increase of p due to an increase of velocity (v) or to an increase of relativistic mass (m) 4 /49 G. Chiodini - May 2015

5 How a particle is accelerated relativistic mass m = γ m 0 mass at rest β = v c speed relative to speed of light (c) γ = 1 1 β 2 Relativistic factor of dilatation β = 1 1 γ 2 The relativistic mass ( than time and energy ) tends to infinity for speed near to the speed of light c = 300,000 km/s the speed of light is an insurmountable limit. In relativistic regime is more correct to speak of increase of energy than acceleration because the speed saturates at β 1, γ 5 /49 G. Chiodini - May 2015

6 Kinetic and relativistic energy Classic mechanics (Newton)! The kinetic energy T of a particle is quadratic in the velocity and proportional to the rest mass. T = m 0v 2 2 = E Relativistic mechanics (Einstein) The relativistic energy E of a particle is the hypotenuse of a right triangle having as cathets the rest mass and the moment relativistic. The kinetic energy T is defined ad the difference between the relativistic energy and the energy at rest E 0 =m 0 c 2 m 0 c 2 pc E = (m 0 c 2 ) 2 + (pc) 2 T = E m 0 c 2 = E E 0 6 /49 G. Chiodini - May 2015

7 Potential energy U=mgh,T=0 The gravitational force on earth is F=mg where g=9.8m/s 2 is e constant. The work L is the product between Force and Displacement L=Fh=mgh and it corresponds to the potential energy U of the gravitational field. U=mgh/2=T The total energy E=U+T is constant The potential energy U=mgh is converted in kinetic energy T=1/2mv 2 during the body fall-down U=0,T=mgh v = 2gh 7 /49 G. Chiodini - May 2015

8 Electric forces and fields Attractive and repulsive electrical forces occur easily by rubbing Matter electrifies when atoms of matter loose electrons ( + ) or gain electrons ( - ) electrons The electric field E acts on the charge q with the electric force F=qE The electron charge is 1.6E-19 Coulomb 8 /49 G. Chiodini - May 2015

9 Electrostatic energy and elettronvolt (ev) The electric potential V[=Energy/Charge] is the work done on the unit charge q=1c V=L/q=Fh/q=qEh/q=Eh V is measured in Volt = Joule/Coulomb The potential energy is U=qV 1 Volt battery It is practical to use as energy unit the elettronvolt, which is equal to the energy acquired by an electron moving in a potential difference of 1 Volt: 1eV= (e) (1V) = (1.6E-19 C) x (J / C) 1eV=1.6E-19 J 9 /49 G. Chiodini - May 2015

10 Electron and proton mass The mass can be measured in energy by multiplying for c 2 Often you write m(gev/c 2 ) me=9.1e-31 kg mec 2 =9.1E-30 kg (3E8) 2( m/s) 2 =81E-14 J mec 2 /e=81e-14 J / 1.6E-19 C = 50E5 ev = 0.5MeV Mp=1.7E-27kg 1870xme=0.94GeV 1GeV=1000MeV, 1MeV=1000keV, 1keV=1000eV 10/49 G. Chiodini - May 2015

11 Electron and proton momentum The momentum can be measured in energy by multiplying for c elettrone me=0.5mev/c 2 Often you write p(gev/c) T=E-E 100keV 1MeV 10MeV 100MeV β=v/c 0,55 0,943 0,9975 0, γ 1, protone Mp=1GeV/c 2 T=E-E 1MeV 10MeV 100MeV 1GeV β=v/c 0,0447 0,0197 0,416 0,866 γ 1,001 1,01 1,1 2 The electron energy increase above 1 MeV is mostly due to relativistic mass increase The proton velocity increase is important up to thousand of MeV Use formula of slide 5,6 and 7 to calculate the 2 nd and 3 rd columns from the 1 st one. 11/49 G. Chiodini - May 2015

12 Pre-accelerators era 12/49 G. Chiodini - May 2015

13 Particle sources A hot filament ( K ) which acts as a cathode in vacuum emits electrons ( - ) that are accelerated by a potential difference ( Ua ) and strike a metal target ( A) which acts as an anode emitting X-rays. The target is maintained at a temperature lower than the melting point by means of a liquid coolant ( W ). In 1895 Lenard builds the C R T f o r s c a t t e r i n g experiments on gas by accelerating electrons. The CRT is sold to Rontgen who discovers that X-rays were produced 13/49 G. Chiodini - May 2015

14 Natural radioactivity The alpha radiation emitted by a natural source natural is transformed into a collimated beam and directed towards a thin sheet of gold through a hole of the lead shield. A fluorescence screen reveals the deflection at large angles of alpha radiation discovering in the atom the presence of a small nucleus that contains almost all the mass ( the atomic nucleus ). In 1906 Rutherford bombards mica and gold sheets with natural alpha radiation of a few MeV energy In 1919 Rutherford i n d u c e s a n u c l e a r reaction with natural alpha radiation 14/49 G. Chiodini - May 2015

15 Electrostatic accelerators era 15/49 G. Chiodini - May 2015

16 Electrostatic accelerator Dome at high electric voltage V Accelerating tube Grounded mechanical base Target Source of ions extracted from a discharge tube Final energy = Initial energy + (ion charge) x V It is necessary to have a DC (direct current) high voltage generator: Cockcroft-Walton s voltage multiplier Van De Graaff s generator 16/49 G. Chiodini - May 2015

17 Cockcroft-Walton multiplier Rutherford pushes for accelerators exceeding MeV but this was not in those times reach In 1928 Gamov predicts that 0.5 MeV may be enough to induce nuclear reactions thanks to the tunnelling effect. In 1932 Cockcroft and Walton reach 0.7 MeV and split lithium atom with protons accelerated to 0.4 MeV: ( Li7 + p He4 + He4 ) 17/49 G. Chiodini - May 2015

18 Voltage multiplier Diodes D1 e D2 conduct c u r r e n t i n t h e a r r o w direction only. The capacitors C1 and C2 charge-up to maximum voltage by the diodes The output voltage is the sum of the capacitor voltages: V out =V C1 +V C2 =2V INP n stages: V out=2nv INP 18/49 G. Chiodini - May 2015

19 Cockroft-Walton at FNAL in Chicago The AC transformer of a few kv is not shown In the cubic structure the electrons are added to hydrogen atoms to form negative ions Negative ions are passed into the top left tube towards the 0.75 MV Cockroft - Walton generator The Cockroft-Walton generator is on the left with a dome on the top The capacitors are most of the vertical blue cylinders The diodes are the diagonal cylinders diagonal The metallic balls and toroids prevent the formation of corona and/or arc discharges between connection points 19/49 G. Chiodini - May 2015

20 Van de Graaff s generator In the early 30's Van de Graaff builds its highvoltage generator of up to 1.5 MV. These generators can operate up to 10 MV, provide stable beams, highly directional and w i t h l o w e n e r g y dispersion. 20/49 G. Chiodini - May 2015

21 Tandem Van de Graaff E = V + zv Negative ions gain energy V at the HV terminal where they are transformed in neutral atoms (z=0) and positive ions (z=1,2, ) by the stripping gas. The doubling of energy is achieved with a very clever idea : change the sign of the accelerated particles charge and use a second generator with opposite polarity These generators can operate up to 10 MV, provide stable beams, highly directional and w i t h l o w e n e r g y dispersion. 21/49 G. Chiodini - May 2015

22 The limit of electrostatic accelerators The limit of electrostatic generators is of about 10 MV beyond which electrostatic breakdown of electrical insulation occurs and you can not increase energy by putting more generators in cascade The electrostatic field is conservative and energy gain can not be boost through multiple passes 22/49 G. Chiodini - May 2015

23 True accelerators era 23/49 G. Chiodini - May 2015

24 Linear and circular accelerators Circular Linear but time variable fields must be used 24/49 G. Chiodini - May 2015

25 Linear accelerators 1. Cascade of identical accelerating structure. 2. Time variable electric fields to avoid an increase of voltage going from one accelerating structure to the next one. 25/49 G. Chiodini - May 2015

26 Wideroe s linac E=0 +! E<0 E=0 E=0 +! E>0 +! E<0 + - E=0 The beam is extracted in bunches. Only synchronous particles are accelerated ( next slide ) In 1924 Ising proposes to use variable electric fields between consecutive cylindrical conductor (drift tubes) to boost the energy beyond the maximum voltage of the system ("true" accelerator). In 1928 Wideroe demonstrates the Ising s principle by a 1MHz radio frequency oscillator of 25 kv amplitude accelerating potassium ions at 50 kev. 26/49 G. Chiodini - May 2015

27 Synchronous condition E(t) = E 0 cos(2πft) L = vt 2 π mode E = E L 0 = v 0T 2 t E = E L 1 = v 1 T 2 E = E 0 L 2 = v T 2 2 t2=t0+t/2 t2=t0+t 27/49 G. Chiodini - May 2015

28 Alvarez s linac L = vt synchronous condition: 2π mode The drift tubes are limited to 10 MHz becoming antennas and dissipating energy in space. With this frequency upper limit and at high energy the length of the tubes becomes prohibitive In 1946 Alvarez surrounds the drift tubes with a RF Resonant Cavity supplied by an external High Power- High Frequency RF source that generates electromagnetic waves at M H z f r e q u e n c y ( R a d a r Technology of the 2nd World War) 28/49 G. Chiodini - May 2015

29 Electromagnetic waves E(t,z) = E 0 cos(2π t T 2π x λ ) Frequency f = 1 T Wavelength λ = c f = Tc f=10mhz T=100ns λ=30m f=200mhz T=5ns λ=1.5m f=3ghz T=0.33ns λ=0.1m An electromagnetic wave in vacuum is constituted by mutually orthogonal electric and magnetic fields varying sinusoidally in time and space and orthogonal to the propagation direction. NB : In a resonant cavity the electric field acquires a component parallel to the propagation direction and can accelerate charged particles. 29/49 G. Chiodini - May 2015

30 Phase velocity E(t,z) = E 0 cos(2π t T 2π x λ ) The phase velocity is determined by the apparent motion of the wave crest. E(t,z) = E 0 cos(2π t + Δt T 2π x λ ) t t fase = cos tan te = ϕ = 2πt T 2πx λ 2πt T 2πx 2π(t + Δt) 2π(x + Δx) = λ T λ Δt T = Δx λ Δx Δt = λ T v fase = Δx Δt = c NB : In a resonant cavity the phase velocity v fase of an electromagnetic wave is less than the speed of light and can accelerate the particles satisfying the synchronous (or resonant) condition v particella = v fase. What happen in a waveguide? 30/49 G. Chiodini - May 2015

31 Dispersion relation of: vacuum, wave guide, cavities 31/49 G. Chiodini - May 2015

32 The limit of Linacs The use of radio frequency allows to have zero potential at both accelerator ends avoiding the system breakdown An unlimited number of drift tubes spaced by acceleration gaps can be cascaded. The linac becomes impractical when the energies is too high because the length becomes unrealistic 32/49 G. Chiodini - May 2015

33 Circular accelerators 1. Use time-varying fields to increase energy along closed orbits. 2. Deflection fields in several regions needed to keep particles in closed orbits. 33/49 G. Chiodini - May 2015

34 Magnetic fields Current loop is equivalent to magnetic compass needle The Earth is a large magnet interacting with the magnetic compass needle and orienting the needle from north to south The magnetic field B is generated by a macroscopic electric current (coil) or by a microscopic electric current (material ferromagnetic domains) of the materials ) and it is orthogonal to it. The magnetic field generated by a coil ( or by a magnet ) generate a force acting on other coil ( or other magnet ). The magnetic poles of a coil ( or of a magnet ) repel ( attract ) each other if generated by currents having the same direction ( opposite ). The magnetic poles of a coil ( or of a magnet) can not be separated (there are no magnetic monopoles ) then the magnetic force acting on a coil ( or on a magnet) tends to make it rotate ( like the needle of a compass ). 34/49 G. Chiodini - May 2015

35 Electric and magnetic force acting on a charged particle v E F elettrica = qe The electric force is parallel to the electric field and only the component parallel to particle velocity can accelerate the particle B v F magnetica = qvb The magnetic force is orthogonal to particle speed and to the magnetic field, than it doesn t accelerate the particle In relativistic regime v ~ c and the magnetic force becomes very efficient in deflecting the particle 35/49 G. Chiodini - May 2015

36 Uniform circular motion A particle of mass m during a uniform circular motion of radius ρ with tangential velocity v is subject to an acceleration towards the center equal to: a=v 2 /ρ (centripetal acceleration). The Newton s law of force implies that to a centripetal acceleration corresponds to a centripetal force: centripetal acceleration = mass x centripetal acceleration v F centripeta = ma centripeta = m v2 ρ ρ F centripeta a = v2 ρ m F centriguga = ma centripeta F centripeta + F centriguga = 0 36/49 G. Chiodini - May 2015

37 Uniform circular motion in magnetic field Centripetal force = Magnetic force F centripeta = qvb F centripetal F centrifuga = ma = m v2 ρ = pv ρ pv ρ = qvb p q = ρb p(gev / c) magnetic rigidity z = 0.3ρ(m)B(T) p q = ρb cp / e q / e = cρb p(ev / c) z = cρb p(gev / c) z = cρb 10 9 p(gev / c) z = ρb 10 9 q=ze where z is the charge in unit of the electron charge 37/49 G. Chiodini - May 2015

38 The cyclotron In 1929 Lawrence designs the famous cyclotron : a linac wrapped on itself In 1931 his student Livingston builds a demonstrator accelerating hydrogen ions up to 80 kev In1932 Lawrence builds a cyclotron accelerating protons up to 1.25 MeV and splits atoms 38/49 G. Chiodini - May 2015

39 The Lawrence s cyclotron An electromagnet generates a magnetic field which rotates the charged particles. On two D-shaped hollow containers an alternating voltage is applied synchronised with the charged particles arrival. At each charged particle passing between the two D s the particles are accelerated. The charged particles released from the source at the centre between the two D s spiral-out until they are extracted and sent to the target. 39/49 G. Chiodini - May 2015

40 Cyclotron synchronous condition Revolution period T = 2πρ v = 2πρ p / m = 2πρ qρb / m = 2π m qb Revolution frequency f = 1 T = 1 qb 2π m (isochronous not synchronous, see later) The beam is extracted in bunches. Only synchronous particles are accelerated. In the non-relativistic regime f is constant and the accelerated particle remains synchronous with the radio frequency ( suitable for protons and not for electrons) 40/49 G. Chiodini - May 2015

41 The betatrons In 1923 Wideroe designs the betatrons discovering the famous rule 2 to 1, but his prototype does not work (vacuum problems) In 1940 Kerst reinvents the betatron and builds one for electrons up to 2.2 MeV In 1950 Kerst builds the largest betatron in the world for electrons up to 300 MeV 41/49 G. Chiodini - May 2015

42 The betatron A pulsed electromagnet generates a variable magnetic field which rotates the charged particles. The charged particles circulate in a circular tube and concatenate the variable vertical magnetic field The guide magnetic field keeps the particles in a circular orbit and the mean magnetic field accelerates the particles by magnetic induction The mean field and the guide field must satisfy the rule 2 : 1 to keep the synchronous particles (Wideroe s principle) 42/49 G. Chiodini - May 2015

43 Lenz s law of magnetic induction B= EXTERNAL MAGNETIC FIELD changing in time S=surface with boundary C E=induced electric field V = ΔΦ max Δt C=closed curve The alternator conver ts m e c h a n i c a l e n e r g y i n t o electrical energy E(t) = E 0 cos(2πft) B(t)=Bmax = 2πfB max Ssin(2πft) The work of the electric field along a closed curve C of length L is equal to the rate change of the magnetic flux Φ crossing the surface S. V = EL = Φ max T = B maxs T The electric field induced by the variable magnetic field is orthogonal to it and capable of accelerating a charged particle along the closed trajectory NB: The direction of the electric field is such to induce a current which generates a magnetic field opposite to the field variation. 43/49 G. Chiodini - May 2015

44 Ratio 2:1 Acceleration E poloidale 2πρ = Φ max T = B medio max πρ 2 T medio ρ p = F poloidale T = ee poloidale T = eb max 2 Rotation T p = eρb guida B guida = 1 2 B medio max The extracted beam is continuos (during the spill) T is of the order of milliseconds (spill period) 44/49 G. Chiodini - May 2015

45 The synchrotron In 1943 Oliphant combines three concepts : acceleration with RF resonators, variable frequency, pulsed guide magnetic fields. In 1944 McMillan and Veksler independently propose the synchrotron with Phase Stability In 1946 Goward and Barnes are the first to build a synchrotron in UK In 1952 several groups invent the Strong Focusing Plenty of room for injection, experiments, extraction, RF cavities... thanks to the "strong focusing" of the quadrupole ( next lesson ). In 1956 MURA in US proposes to increase the beam intensity by Stacking In 1961 Touschek creates the first singleloop electron-positron collider (e+-e- ) 45/49 G. Chiodini - May 2015

46 Deflection of charge particles B = µ 0nI h where μ0=4π10-7 H/m, n=number of turns, I=coil current, h=pole gap Magnetic deflection C-shaped magnetic dipoles employed as particle field guide in synchrotron (excellent in relativistic regime) p(gev / c) z = 0.3ρ(m)B(T) magnetic rigidity E = V h v h v h << v V=voltage and E=vertical electric field Electrostatic deflection Parallel plates ( V ~ 200kV ) used to inject beams in the synchrotron ( excellent for low energy ) θ = v h v = mv h mv = qet mv = qvl mv 2 h 46/49 G. Chiodini - May 2015 L θ

47 (synchronous, n o t isochronous) Synchrotron cycle p(gev / c) z Acceleration phase = 0.3ρ(m)B(T) Circular orbit Syncrotron cycle The beam is in bunches T is of the order of hours or days RF B RF=OFF B=constant f r = 2πv ρ = f n Synchrotron condition: the radio frequency f must be an integer of the rotation frequency fr The name synchrotron is due to the fact that the frequency f of the RF cavities should be adjusted during the acceleration to meet the synchrony condition and the magnetic field B has to be increased during acceleration to keep the particle in orbit. 47/49 G. Chiodini - May 2015

48 Electro-syncrotron in Frascati ( electrons at GeV) 4 dipoles week focusing! Very little space for injection, experiments, extraction, radiofrequency, It needs a "strong focusing" quadrupole ( next lesson ). 48/49 G. Chiodini - May 2015

49 Classification Electrostatic accelerators Cockcroft-Walton Van De Graaff Tandem Accelerators with time-varing electric field Induction accelerators betatrons Radiofrequency accelerators Linac Cyclotron Synchrotron Conservative electrostatic force Betatron: Unbunched E poloidal EL = V Electromagnetic induction force V = EL = B max S T Resonator: Bunched E axial 49/49 G. Chiodini - May 2015