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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 [email protected]