FUNDAMENTAL SHORT TIME-SCALE RELATIVISTIC PHYSICS: COLLECTIVE PHENOMENA. PARTICLE ACCELERATION AND PRODUCTION IN FEMTOSECOND LASER-MATTER INTERACTION

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1 FUNDAMENTAL SHORT TIME-SCALE RELATIVISTIC PHYSICS: COLLECTIVE PHENOMENA. PARTICLE ACCELERATION AND PRODUCTION IN FEMTOSECOND LASER-MATTER INTERACTION Anton Baldin Institute for Advanced Studies, Dubna University Joint Institute for Nuclear Research May, 00

2 Outlook Relativistically invariant self-similarity approach in nuclear physics. Similarity of extreme states of nuclear matter and ultrashort laser-matter interaction. Correlation between geometric characteristics in Lobachevsky space and measurable parameters.

3 Chen Ning Yang Symmetry and Physics,988 SYMMETRY INVARIANCE CONSERVATION LAWS GAUGE SYMMETRY SYMMETRY DICTATES INTERACTION OTHER CONSEQUE NCES QUANTUM NUMBERS SELECTION RULES STRONG FORCE ELECTRO- MAGNETIC FORCE WEAK FORCE GRAVITY FORCE Schematic diagram illustrating the role of symmetry in fundamental physics.

4 Self-similarity is a special symmetry of solutions which consists in that the change in scales of independent variables can be compensated by the self-similarity transformation of other dynamical variables. This results in a reduction of the number of the variables which any physical law depends upon.

5 x q P q This is the way in which the self-similarity laws following from dimensionality considerations in the region P >> M are extensively applied

6 P xp P P i P P xp P P i P q q xp P i kl MM k l k q xp q x P M x q P q

7 X P A X P A X P X P P P i M The relationship between X and X is described by the conservation laws written in the form XMu XMu Mu MnXu MnXu Mkuk k 4 Essentially, we are using the correlation depletion principle in the relative four-velocity space which enables us to neglect the relative motion of not detected particles, namely the quantity kl M k M l k in the right-hand part of the above equation.

8 X X X M M 4 M X M M M X X X X M M M M M 4 4 p p p p p In the case of production of antiparticle with mass M, the mass M 4 is equal to M as a consequence of conservation of quantum numbers. In studying the production of protons and nuclear fragments M 4 = M as far as the minimum value of corresponds to the case that no other additional particles are produced. The values X and X obtained from the minimum are used to construct a universal description of the A-dependencies. S P P E d d p X X C A A f

9 Cumulative processes inv A A [mb Gev - c sr - ] E- E-4 E-5 E-6 E-7 E-8 E-9 45 Gev 59 o Al Ti Mo W 0.4 GeV 97 o Al Cu Ta E S.V.Boyarinov, et al. Yad. Fis., v.57, N8, (994), O.P.Gavrishchuk et al. Nucl. Phys., A5 (99) 589.

10 inv A A [mb Gev - c sr - ] Twice cumulative A+A--->P,K+... _ GeV/n Angle P dc.65 4 o CC.65 4 o CCu.65 4 o SiSi.0 0 o SiSi.65 0 o _ K dc.5 4 o CC.5 4 o SiSi.0 0 o SiSi.4 0 o SiSi.0 0 o CaCa.0 0 o Jim Carroll Nucl. Phys. A488 (989) 9. A.Shor et al. Phys. Rev. Lett. 6 (989) 9. A.A.Baldin et al. Nucl. Phys., A59 (990) 407. A.A.Baldin et al. Rapid Communications JINR, -9 (99) 0.

11 inv A A [mb Gev - c sr Twice cumulative A+A--->P,K +... _ GeV/n 0 o P NeCu.9 NeSn.89 NeSn.69 NeBi.87 NiNi.85 NiNI.66 _ K NeCu.9 NeSn.89 NeSn.69 NeSn.49 NeBi.87 NiNi.85 NiNi.66 A.Schroter et al. Z.Phys. A50, (994), 0-.

12 Inclusive pion spectra (various experiment types) 0 4 C+ 8 Ta.65 G ev/n 0 0,5 0,45 0,60 0,00 0,0 0 inv /A A Ne+ 64 Cu, 9 Sn, 09 Bi.5-.9 GeV/n 58 Ni+ 58 N i.7-.9g ev/n

13 Inclusive pion spectra in selected high-multiplicity events Mg+ 4 Mg----> <N >=8.4 inv /A A in A.A.Baldin, E.N.Kladnitskaya, O.V. Rogachevsky, JINR Rapid Comm., (999), N. [94]-99, p.0. M.Kh.Anikina, et al., Phys. Lett. B., (997), v.97, p.0.

14 Antimatter production c sr - ] ivn A A [mb GeV - 0 p(40 GeV)+Be--->h +... (0 o ) p anti p d anti d t ( He) anti t ( He)

15 0 0 4 Mg+ 4 Mg----> <N >=8.4 inv /A A in A.A.Baldin, E.N.Kladnitskaya, O.V. Rogachevsky, JINR Rapid Comm., (999), N. [94]-99, p.0. M.Kh.Anikina, et al., Phys. Lett. B., (997), v.97, p.0.

16 Fundamental short time-scale relativistic physics: new collective phenomena Laser powers > W/cm ; Times <00 fs; Electron densities >0 0 cm - ; High efficiency (~0%) Quasi-monochromatic electron spectrum Low emittance Very short acceleration distance (00µm mm). Mangles et al Nature vol.4 0 September 004 pp Geddes, Esarey et al Nature vol.4 0 September 004 pp Pukhov, Malka et al Nature vol.4 0 September 004 pp

17 4 P P xp xp E 4 cos M E E M P E E x C exp C inv exp C X C inv

18 electron momentum [MeV/c] 5 4 Energy 5 [MeV] 0 0, , 0,700 0,67 0,8 0,400 0,967 0,45 0,500 0,5667 0,6 0,6800 0,767 0,79 0,8500 0,9067 0,96, Lab. angle [degree]

19 electron momentum [MeV/c] Lab. angle [degree] Energy 0 [MeV] 0,000 0,6000,00,600,00,600,00,600 4,00 4,600 5,00 5,600 6,00 6,600 7,000

20 0 Energy 0 [MeV] electron momentum [MeV/c] angle [degree] 0,000,00 4,00 6,00 8,00 0,0,0 4,0 6,0 8,0 0,0,0 4,0 6,00

21 electron momentum [MeV/c] Lab. angle [degree] Energy 00 [MeV] 0 5,00 0,00 45,00 60,00 75,00 90,00 05,0 0,0 5,0 50,0 65,0 80,0 95,0 00,0

22 Relativistic pair production: three steps Generation of MeV electrons in subcritical laser plasma 0 8 W/cm ; n n exp( x / ) ; n c 0 / cm ; 0mkm e c dn e de 0 E exp(. E) Bremsstrahlung conversion of MeV electron energy into MeV photons in a high-z solid target photons with the energy higher than MeV e+e- pair production (photonuclear reactions) 0

23 e+e- pairs 0 MeV e e e e ,005 inv (e - e - ->e +...)/ inv (e - e - ->e -...) 0,004 0,00 0,00 0,00 0,000 0,000 0,00 0,00 0,00 0,004 0,005 0,006 0,007 0,008 0,009 0,00 E kin [GeV]

24 inv C exp C inv e - +e - ->e + (at 0 0 )+(e - +e - +e - ) inv e - +e - ->e + (at 0 0 )+(e - +e - +e - ) E kin e - 5 MeV 0 MeV 0 MeV 50 MeV E kin e - 5 MeV 0 MeV 0 MeV 50 MeV 0, 0,0 0,000 0,00 0,004 0,006 0,008 0,00 Lab. momentum positron [GeV/c] 0,000 0,00 0,004 0,006 0,008 0,00 Lab. momentum positron [GeV/c]

25 protons Momentum, MeV/c Protons accelerated by MeV "photons" 0,8E-5,6E-5,544E-5 4,75E-5 5,906E-5 7,087E-5 8,69E-5 9,450E-5 Momentum, MeV/c Protons accelerated by 0 MeV "photons" 0,594E-4,87E-4 4,78E-4 6,75E-4 7,969E-4 9,56E-4 0,006 0, Angle (lab.frame), degrees Angle (lab.frame), degrees

26 Self-similar solution connects the initial and final states. Initial state: intensity (energy); frequency; phase; duration; geometric dimensions of acting volume; target density, Z, A, temperature Prepulse (dynamic target preparation). Final state: fraction of four-momentum transferred; angular, energy spectra of registered radiations; time characteristics of final state. The goal of the self-similarity approach is to reduce the number of variables = find a symmetry in the phenomenon of transition from initial to final state.

27 Lobachevsky Space X P A X P A h Longitudinal rapidity y y ln E E p p defect Transverse mass Transverse rapidity Angle of Parallelism m T m p T mt ch h m ( h) arctg L perimeter e h

28 Proton distribution for two angular intervals in p(0gev/c)+c N p(0 GeV/c)+C->p >.6 [rad] <. [rad] h y A. A. Baldin, E. G. Baldina, E. N. Kladnitskaya, O. V. Rogachevskii, Phys.Part.Nucl.Lett., vol., no. 4, 7-6 (004).

29 Normalized distributions of defects of triangles formed by all combinations of protons and all combinations of mesons registered in p(0gev/c)+c N 0. p exp. p sim. exp. sim. Note, that the model adequately reproduces inclusive spectra of both protons and - mesons. The distribution of trios of -mesons, however, differs noticeably from experimental data defect

30 defect p(0gev/c)+c-> perimeter defect perimeter

31 It is important to underline that, unlike the Euclidean space, the area-to-perimeter ratio for triangles in the Lobachevski space is limited. 0,8 protons protons 0,6 0,8 0,6 0,4 0, defect/perimeter defect/perimeter 0,4 0,0 0,08 0,06 0,04 0, 0,0 0,08 0,06 0,04 0,0 0,0 0,00,6 pionsdp 0,00,8,0,,4,6,8 4,0 4 perimeter 6 8 perimeter π-c (40 GeV) 0

32 Analysis of Lobachevsky geometry defect/perimeter,0 0,8 0,6 0,4 dp dp4 dp5 dp0 dp00 dp000 0, 0, perimeter Regular polyhedrons with n=, 4, 5, 0, 00, and 000 inscribed in a circle with an increasing radius

33 tg ( h) L e h ( h) L arctg e h h α ρ β h L

34 h p(0gev/c)+c-> p(0gev/c)+c->p y N L ( )= ,00 0,05 0,0 0,5 0,0 0,5 0,0 L -

35 pc (0 GeV) Protons, GeV/c protons Protons, protons 6.5 º N P [GeV/c] [degr] Lab. sys. pions 00 N Pions, 500 MeV/c Pions, 6.5 º N N ,0 0,5,0,5,0,5,0 P[GeV/c] [derg] Lab. sys.

36 n+p-> 5. GeV/c MeV/c.8 GeV/c MeV/c. GeV/c MeV/c.7 GeV/c MeV/c.4 MeV/c ,0 0, 0, 0, 0,4 0,5 0,6 0,7 0,8 0,9,0 L (h)-

37 Directed Nuclear Radiation cos th sh h th,p rad, GeV/c 0, 0 00 p GeV/c

38 Directed Nuclear Radiation P+C->pions at 0GeV,4 0 9, 8 P GeV/c,0 0, ,6 0,4 0, 0,04 0,06 0,08 0,0 0, 0,4 L - 0 0,06 0,08 0,0 0, 0,4 L -

39 sh(h ) 4,0,8,6,4,,0,8,6,4,,0,8,6,4,,0 0,8 0,6 0,4 0, π-c (40 GeV),0 0,000 0,005 0,000 0,005 0,000 0,005 0,0040 0,0045 L (h )- f h L h arctg th th sh arctg sh h sh h th h

40 Lobachevsky Space n+p-> - 5GeV h 00 y Z Axis defect sh(h) ,6 0,8,0 0,4 0,,8,,4,6 defect

41 Common features of relativistic nuclear physics and ultrashort laser-matter interaction: Extreme states of matter; Relativism; Collective phenomena; Multiparticle interactions.

42 The XX International Seminar on High Energy Physics Problems "Relativistic Nuclear Physics and Quantum Chromodynamics", organized by the Joint Institute for Nuclear Research will be held October 4-9, 00 in Dubna, Russia. Important Deadlines Abstracts submission before August, 00. Abstracts should be sent to