Little bang.. On earth experiments emulating time between 0.001-1 second after the BIG_Bang PartI : actors (particles) Tools (accelerators)
Can we restore creation of matter in experiments on Earth?
Structure of the matter Elektromagnetic interaction Strong Interaction If protons and neutrons have diameter of 10 cm then quarks and electrons would be smaller than 0.1 mm, but diameter of the atom would be 10 km!
Structure of matter the most elementary we know.. 3 families of particles: Leptons & Quarks baryons: 3 quarks d u u proton Mesons: quark-antiquark Every particle has its anti-partner (anti-particle) Baryons and mesons (hadrons) are kept by strong interactions which increase with the distance and confining quarks inside q q
Proton Quarks are bound inside proton (nucleon) Can we liberate quarks? Nucleus consist of nucleons Quark-Gluon plasma a new form of nuclear matter ~ 1 µs after the Big_Bang T 1 GeV! Comparable to mass of nucleon!
Time Quark Gluon Plasma Nucleons Stars/Galaxies Nuclei Atoms Today Big-bang 10 6 sec 10 4 sec 3 min 13.5 billions of years Collisions of high Energy Nuclei can produce enough Energy to liberate quarks confined inside hadrons
Collision of 2 heavy nuclei Au Au Nuclear matter in nucleus: density of matter in nucleus is ρ= 0.17 nucleon/fm 3 ~ 10 17 kg/m 3! density of energy = m p * ρ= 0.16 GeV/fm 3 If two Au nuclei are accelerated to v ~ 0.999c E = 200 GeV/nucleon they look like this.. Physicist estimate that Creation of Quark-Gluon Plasma requires: ρ 1.2 /fm 3 ε 1 GeV/fm 3 T 170 MeV collision Explosion plasma creation of particles end of expansion Time of reaction ~10-22 s
Its mass is increasig ~ 7000 times! It life time is getting longer ~ 7000 times! c If we approach speed of light We have to consider relatyvistic effects (A. Einstein) consequences: Mass of partciles are increasing : m = γ m 0 γ = 1 1 v c 2 2 Length along the direction of movement is decreasing: l= l 0 / γ Time is passing longer t = γ t 0 For example for particle with v= 0.999999991 c
How to accelerate particles? In the homogenous Electric field with the strength E partcile acquire energy : = q * E*d (distance) Imagine that we have Electric field generated as a wave changing along the path of particle with q chargé +q: 2π E = E0 cos(2πf t x) λ <a href="big_bang_i.pdf">part I 1a</a><br> f frequency λ - wave length x + means positive (repulsion ) - acceleration -means negative (attraction) slowing down
Volatage L n is the length of n-the electrode V n particle velocity in the n-th electrode For constant acceleration we must have: isolator electrodes or (for non-relativistic)
How to keep particle on a closed trajectory? Most easy is to keep it on a cirlce because of the Lorentz force F = q( v B) = mv R 2 Magntetic Field with the strength B produce force F with a direction towards centrum of the circle cyclotron ω = 2π/T R = p / (q*b) B Constant cycling time! Increasing radius with energy.. Beam deflection
Most effective realization is an accelerator with constant radius constructed in form of a ring - Synchrotron Acceleration by electric field in section 1 Top view Side view Magentic filed created by electromagnets so called dipoles - bending particles in sections 3 Field in magnets is increasing in time to match increasing energy of particles Field in magnets is only applied during acceleration time
These principles are used in design of largest accelerators in the word TEVATRON 20 km from Chicago (USA) 2 rings for protons and antyprotonów with R = 1km. Energy: 1 TeV (1000 GeV!) per particle Large Hadron Collider (LHC) near Geneva (CH) 1 ring for 2 beams of protons with R = 4.3 km. Energy 7 TeV (1000 GeV!) each
Tunnel : 175 m underground LHC SPS LargeHadronCollider : protons are accelerated to 0.999999991 c within 20 minutes, 10 5 revolutions, each revolution gives few MeV kick in rings kept at the temperature of T=1.9 K Final energy of protons is 7 TeV and 570 TeV for Pb ( it corresponds to a macroscopic Energy of 5.9µJ) 2 proton beams are crossing every 25 ns
Magnets in LHC Bendig dipols Superconducting (NbTi) in T= 2K B=8.3 T needs current of 11 850 A 1232 magnets,35 tons each and..0.5 mln CHF Vacuum tube thermoisolation Magnet coils 2 pipes with protons Magnet Steel yoke Liquid helium 5-10 K Liquid helium 1.8 K
Magnets in LHC quadrupols -focusing lens. Focusing beam like lens in optics One QUAD magnet is focusig in one direction (i.e horizonthal) and defocusing in the other (i.e vertical) Putting several magnets with alternating focus onbe achieves netto focus in both directions
What Energy can be achived in collisions Four vector of energy momentun p µ ( pp, E) pp μμ pp μμ = pp pp EE 2 = mm 2 (cc = 1) Length of the four-vector of two particles is an invariant quantity denoted s = (E*) 2 stationary target one particle (target) is at rest Collider two antiparallel particles with higher Energy E ~ p If M << E
Production of new particles Production of new particle X in the reaction Nucleon+Nucleon->Nucleon+Nucleon+X X=a new meson Energy required to produce a partilce with mass Mx can be calculated in the Centrum of Mass Frame (CMS) (system where total incoming momentum =0) of 2 colliding particles as s = 2*M N + M X Some new particles can be created only in pairs to conserve some quantity like : lepton numer (i. e+e-), i.e p+p->p+p+e+ + e- (L=0) baryon number (proton antyproton), p+p -> p+p + n + anty n (B=2) strangeness (new flavour related to Production of s quarks) p+p ->p + K + K+ =(u, anty s) Strangeness S =-1, Λ (u d s) Strangeness S =1, total S=0 Charm (similarly for particles containing charm) + Λ
Accelarators (protons and nuclei) in word GSI/ FAIR AGS SPS RHIC (collider!) LHC (collider) E Kin /A [GeV] 2 (10 in 2022) 10-15 40-200 100 2700 [GeV] 2.7 4.5 8.8-19.4 200 5500 S NN
How to identify a particle? Stable particles (life time is larger than a typical flight time through detectors ~ few ns) mm = pp = pp 1 γγγγ ββ2 1 we measure momentum p from deflection of the particle trajectory in the magnetic field of know strangth B and the flight time (Time of Flight- TOF) β=d/tof Unstable particles with a small lifte times we identfy from their decay products (i) and measure their Energy and momenta E i, p i by so called invariant mass reconstruction: mm = EE ii 2 pp ii 2 or from the so-called missing mass : when all particles in the reactions are measured (i) except the one unknown, and we know beam Energy (p) and target (T) mm = EE TT + EE pp EE ii 2 pptt + pp pp pp ii 2
Example of invariant mass reconstruction M decays into 2 particles with known momenta p 1 p 2 and ϒ->µ+ µ- masses m 1, m 2 M inv =sqrt(ppµpp µ ) Decay probability is given by the width of the particles Γ which is also measure of its life time cτ = 1/Γ units (GeV/ h) -1 Force τ [s] Strong 10-23-20 El.Mag 10-20-16 Weak 10-13+3