FUNDAMENTAL SHORT TIME-SCALE RELATIVISTIC PHYSICS: COLLECTIVE PHENOMENA. PARTICLE

ACCELERATION AND PRODUCTION IN FEMTOSECOND LASER-MATTER INTERACTION

Anton Baldin

Institute for Advanced Studies, Dubna UniversityJoint Institute for Nuclear Research

21 May, 2010

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.

OTHER CONSEQUE

NCES

QUANTUM NUMBERS

SELECTION RULES

SYMMETRY DICTATES INTERACTION

CONSERVATION LAWS

SYMMETRY

GAUGE SYMMETRY

STRONG FORCE

ELECTRO- MAGNETIC

FORCE

WEAK FORCE

GRAVITY FORCE

Chen Ning Yang“Symmetry and Physics”,1988

Schematic diagram illustrating the role of symmetry in fundamental physics.

INVARIANCE

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.

This is the way in which the self-similarity laws following from dimensionality considerations in the region P2 >> M2 are extensively applied

qPqx

2

2

2

iPPxPP 121

22

121

iPPxPP

qPP 11

2

22

iPxPq

222

22

2 2 MPxqxPq

qPqx

2

2

2

2 11 kl k l

kM M

3M

1

11 A

PX2

22 A

PX

X M u X M u M u M X u M X u M un n k kk

1 1 1 2 2 2 3 3

2

1 1 2 24

2

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 in the right-hand part of the above equation.

2 11 kl k l

kM M

The relationship between X1 and X2 is described by the conservation laws written in the form

iPPPXPX 12211

21

122122

21 2

21 XXXX

Edd p

C A A fX X3

3 1 1 21 2

X X XMM

MM

XMM

MM

M MMp p p p p

1 2 12 13

134

23

234 4

232

12

In the case of production of antiparticle with mass M3 , the mass M4 is equal to M3 as a consequence of conservation of quantum numbers. In studying the production of protons and nuclear fragments M4 = M3 as far as the minimum value of

corresponds to the case

that no other additional particles are produced. The values X1 and X2obtained from the minimum

are used to construct a universal

description of the A-dependencies.

221 PPS

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.01E-10

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

0.01

0.1

1

10

45 Gev 159o

Al Ti Mo W

10.14 GeV 97o

Al Cu Ta

inv

A1

1 A2

2 [mb

Gev

-2 c

3 sr -1

]

Cumulative processes

S.V.Boyarinov, et al. Yad. Fis. , v.57, N8, (1994) ,1452-1461.

O.P.Gavrishchuk et al. Nucl. Phys., A523 (1991) 589.

1.5 2.0 2.5 3.0 3.5 4.0 4.510-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

in

v A 1

1 A 2

2 [

mb

Gev

-2 c

3 sr-1

]

_ _ A+A--->P,K+... _ GeV/n Angle P

dC 3.65 24o CC 3.65 24o CCu 3.65 24o SiSi 2.0 0o

SiSi 1.65 0o

_ K

dC 2.5 24o CC 2.5 24o SiSi 1.0 0o

SiSi 1.4 0o

SiSi 2.0 0o

CaCa 2.0 0o

Twice cumulative

Jim Carroll Nucl. Phys. A488 (1989) 2192.A.Shor et al. Phys. Rev. Lett. 62 (1989) 2192.A.A.Baldin et al. Nucl. Phys., A519 (1990) 407.A.A.Baldin et al. Rapid Communications JINR, 3-92 (1992) 20.

1.5 2.0 2.5 3.0 3.5 4.0 4.510-10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

in

v A 1

1 A 2

2 [

mb

Gev

-2 c

3 sr-1

_ _ A+A--->P,K +... _ GeV/n 0o

P NeCu1.9 NeSn1.89 NeSn1.69 NeBi1.87 NiNi1.85 NiNI1.66

_ K

NeCu1.9 NeSn1.89 NeSn1.69 NeSn1.49 NeBi1.87 NiNi1.85 NiNi1.66

Twice cumulative

A.Schroter et al. Z.Phys. A350, (1994), 101-113.

Inclusive pion spectra (various experiment types)

0 .5 1 .0 1 .5 2 .0 2 .51 0 -3

1 0 -2

1 0 -1

1

1 0

1 0 2

1 0 3

1 0 4

in

v/A1

A2

1 2C + 1 8 1T a 3 .6 5 G e V /n

1 0 0 ,3 5 0,4 5 0,6 0 0,1 0 0 0,1 2 0 0

2 0N e + 6 4C u ,1 1 9S n ,2 0 9B i 1 .5 -1 .9 G e V /n 5 8N i+ 5 8N i 1 .7 -1 .9 G e V /n 0 0

A.A.Baldin, E.N.Kladnitskaya, O.V. Rogachevsky, JINR Rapid Comm., (1999), N.2 [94]-99, p.20.M.Kh.Anikina, et al., Phys. Lett. B., (1997), v.397, p.30.

Inclusive pion spectra in selected high-multiplicity events

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

10-4

10-3

10-2

10-1

100

10-4 in

24

Mg+24

Mg---->

<N>=8.24

50

150

250

350

450

600

800

1000

1200

1500

inv/A

1 A

2

0.5 1.0 1.5 2.0 2.5 3.0 3.510 -10

10-9

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102 p(240 G eV)+Be--->h +... (0 o)

p anti p d anti d t ( 3He) anti t ( 3H e)

iv

n A1

A2

[m

b G

eV -

2 c 3 s

r -1]

Antimatter production

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

10-4

10-3

10-2

10-1

100

10-4 in

24Mg+24Mg---->

<N>=8.24

50

150

250

350

450

600

800

1000

1200

1500

inv/A

1 A

2

A.A.Baldin, E.N.Kladnitskaya, O.V. Rogachevsky, JINR Rapid Comm., (1999), N.2 [94]-99, p.20.M.Kh.Anikina, et al., Phys. Lett. B., (1997), v.397, p.30.

Laser powers >1019-1020 W/cm2;Times <100 fs;Electron densities >1020 cm-1;

High efficiency

(~20%)Quasi-monochromatic

electron

spectrum

Low emittanceVery

short

acceleration

distance (100µm –

1mm)

1. Mangles et al Nature vol.43 30 September 2004 pp.535-538

2. Geddes, Esarey

et al Nature vol.43 30 September 2004 pp.538-

541

3. Pukhov, Malka

et al Nature vol.43 30 September 2004 pp.541-544

Fundamental short time-scale relativistic physics: new collective phenomena

4311 PPxPxPE

431

333 cosMEEM

PEEx

21 exp

CCinv

21 exp

CXCinv

-30 -20 -10 0 10 20 300

1

2

3

4

5Energy 5 [MeV]

Lab. angle [degree]

elec

tron

mom

entu

m [M

eV/c

]

00,056670,11330,17000,22670,28330,34000,39670,45330,51000,56670,62330,68000,73670,79330,85000,90670,96331,000

-30 -20 -10 0 10 20 300

2

4

6

8

10Energy 10 [MeV]

Lab. angle [degree]

elec

tron

mom

entu

m [M

eV/c

]

0,10000,60001,1001,6002,1002,6003,1003,6004,1004,6005,1005,6006,1006,6007,000

-30 -20 -10 0 10 20 300

2

4

6

8

10

12

14

16

18

20Energy 20 [MeV]

angle [degree]

elec

tron

mom

entu

m [M

eV/c

]

0,2000

2,200

4,200

6,200

8,200

10,20

12,20

14,20

16,20

18,20

20,20

22,20

24,20

26,00

-30 -20 -10 0 10 20 300

20

40

60

80

100Energy 100 [MeV]

Lab. angle [degree]

elec

tron

mom

entu

m [M

eV/c

]015,0030,0045,0060,0075,0090,00105,0120,0135,0150,0165,0180,0195,0200,0

Relativistic pair production: three steps

• Generation of MeV electrons in subcritical laser plasma1018 W/cm2; ; ;

• Bremsstrahlung conversion of MeV electron energy into MeV photons in a high-Z solid target

8·107 photons with the energy higher than 1 MeV

• e+e- pair production (photonuclear reactions)

)/exp( xnn ce mkm30321 /110 cmnc

)2.1exp(103 10 EEdEdNe

e+e- pairs

eeee 3

0,000 0,001 0,002 0,003 0,004 0,005 0,006 0,007 0,008 0,009 0,0100,000

0,001

0,002

0,003

0,004

0,005

inv(e

- e- ->e+ ...

)/in

v(e- e- ->

e- ...)

Ekin [GeV]

00

20

MeV10

0,000 0,002 0,004 0,006 0,008 0,010

1

e-+e-->e+(at 00)+(e-+e-+e-)inv

Lab. momentum positron [GeV/c]

Ekine-

5 MeV 10 MeV 20 MeV 50 MeV

0,000 0,002 0,004 0,006 0,008 0,010

0,01

0,1

1

e-+e-->e+(at 00)+(e-+e-+e-)inv

Lab. momentum positron [GeV/c]

Ekine-

5 MeV 10 MeV 20 MeV 50 MeV

21 exp

CCinv

protons

0 20 40 60 80

10

20

30

40

Angle (lab.frame), degrees

Mom

entu

m, M

eV/c

0

1,181E-5

2,362E-5

3,544E-5

4,725E-5

5,906E-5

7,087E-5

8,269E-5

9,450E-5

Protons accelerated by 1 MeV "photons"

0 20 40 60 80

20

40

60

80

100

Protons accelerated by 10 MeV "photons"

Angle (lab.frame), degrees

Mom

entu

m, M

eV/c

0

1,594E-4

3,187E-4

4,781E-4

6,375E-4

7,969E-4

9,562E-4

0,001116

0,001275

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, temperaturePrepulse (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.

Lobachevsky Space1

11 A

PX

hL earctgh 2)(

1

3

212

13

23

3

1

2

h

y

Longitudinal rapidity

Transverse mass

Transverse rapidity

||

||ln21

pEpE

y

22TT pmm

mmh Tch

321 defect

321 perimeter

Angle of Parallelism

2

22 A

PX

Proton distribution for two angular intervals in p(10GeV/c)+C

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.50

100

200

300

400

500

600

700

800

900

1000

1100

1200

p(10 GeV/c)+C->pN

23

>1.6 [rad]

<1.3 [rad]

1

3

21

2

1

3

2

3

3

1

2

h

y

A. A. Baldin, E. G. Baldina, E. N. Kladnitskaya, O. V. Rogachevskii, Phys.Part.Nucl.Lett., vol. 1, no. 4, 7-16 (2004).

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6

0.1

1

N

defect

p exp. p sim. exp. sim.

Normalized distributions of defects of triangles formed by all combinations of protons and all combinations of mesons registered in p(10GeV/c)+C

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.

6 7 8 9 10 110.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

defe

ct

perimeter

p(10GeV/c)+C->

321 defect

321 perimeter

12,6 12,8 13,0 13,2 13,4 13,6 13,8 14,00,00

0,02

0,04

0,06

0,08

0,10

0,12

0,14

0,16

0,18

defe

ct/p

erim

eter

perimeter

protons

12 14 16 18 20 220,00

0,02

0,04

0,06

0,08

0,10

0,12

0,14

0,16

0,18

defe

ct/p

erim

eter

perimeter

dp

π-C (40 GeV)

pionsprotons

It is important to underline that, unlike the Euclidean space, the area-to-perimeter ratio for triangles in the Lobachevski space is limited.

Analysis of Lobachevsky geometry

0 2 4 6 8 100,0

0,2

0,4

0,6

0,8

1,0de

fect

/per

imet

er

perimeter

dp3 dp4 dp5 dp10 dp100 dp1000

Regular polyhedrons with n=3, 4, 5, 10, 100, and 1000 inscribed in a circle with an increasing radius

h

2 1

3

ρ

α

β

hL ehtg

2)(

hL earctgh 2)(

33312 2 hL

0,00 0,05 0,10 0,15 0,20 0,25 0,300

200

400

600

800

1000

1200

1400

L()=0.0945

N

L-1

p(10GeV/c)+C-> p(10GeV/c)+C->p

1

3

21

2

1

3

2

3

3

1

2

h

y

0,0 0,5 1,0 1,5 2,0 2,5 3,0-100

0

100

200

300

400

500

600

700

N

P[GeV/c]

pions

0 10 20 30 40 50-50

0

50

100

150

200

250

300

350

400

450

N

[derg] Lab. sys.

0 5 10 15 20 25 30-50

0

50

100

150

200

250

300

350

400

N

[degr] Lab. sys.

protons

0 1 2 3 4 5 6 7 8-50

0

50

100

150

200

250

300

350

400

450

N

P [GeV/c]

protonsProtons, 3 GeV/c Protons, 16.5 º

Pions, 500 MeV/c Pions, 16.5 º

pC

(10 GeV)

0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,00

200

400

600

800

1000

1200

2L(h3)-1

5.2 MeV/c 3.8 MeV/c 2.3 MeV/c 1.7 MeV/c 1.4 MeV/c

n+p->GGeV/cGeV/cGeV/cGeV/c

Directed Nuclear Radiation

1 10 100

0,1

1

,

P3

rad,

GeV

/c

p GeV/c

2

12

1cos 1

31

2

th

hshth

0,04 0,06 0,08 0,10 0,12 0,140,2

0,4

0,6

0,8

1,0

1,2

1,4

2L-

P3 G

eV/c

0,06 0,08 0,10 0,12 0,1410

11

12

13

14

15

16

17

18

19

20

L-

Directed Nuclear RadiationP+C->pions at 10GeV

π-C (40 GeV)

12

2,0

12

22

32

0,0010 0,0015 0,0020 0,0025 0,0030 0,0035 0,0040 0,0045

0,20,40,60,81,01,21,41,61,82,02,22,42,62,83,03,23,43,63,84,0

sh(h

3)

L(h3)-

2

21

22

212

11

thhsh

hshtharctg

hsh

tharctghhf L

Lobachevsky Space

1

3

212

13

23

3

1

2

h3

y

1 2 3 4 56

78

0

50

100

150

200

0,20,4

0,60,8

1,01,2

1,41,6

1,8

Z Ax

is

defec

t

sh(h3)

321 defect

n+p->- 5GeV

Common features of relativistic nuclear physics and ultrashort laser-matter

interaction:

Extreme states of matter; Relativism; Collective phenomena;Multiparticle interactions.

• 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, 2010 in Dubna, Russia.

Important

Deadlines• Abstracts submission before August

31, 2010.

Abstracts should be sent to ishepp@theor.jinr.ru