Quantum heat transport induced
by ultra-short laser pulses:
from foundations to applications

1  Introduction

The development of ultraintense laser pulses will allow the study of new regimes of laser-matter interaction . Lasers are now being designated  which will eventually lead to light intensities such that Il2m >> 1019  Wmm2/cm2. Here I is the laser intersity of the laser light and lm is the wavelenght in microns. In such intensities the electron jitter velocity in the laser electric field becomes relativistic: p0/mc > 1, where p0 is jitter momentum, m is electron rest mass and c is the light velocity in vacuum. When such lasers interact with an overdense plasma it has been shown that a large number of relativistic superthermal electrons with energy Ehot:

Ehot ~ é
ë 		  æ
Ö
1+[(Il2m)/( 1.4  1018)]
 
 -1 ù
û 		mc2
(1)
are produced . Hence Ehot > mc2 for Il2m > 4  1018. For even higher Il2m,   Ehot can exceed the pair (e+,e-) production threshold. In the result the interaction of ultraintense laser beams with matter can produce copious electron-positron pair which represents a new state of matter with new thermal and radiative properties drastically different from ordinary plasma . For the moment the production of electron-positron pair was realized in SLAC experiment . In that experiment a signal of 106±14 positrons above background has been observed in collisions of a low-emittance 46.6 GeV electron beam with terawatt pulse from a Nd: glass laser at 527 nm wavelength. The positrons are interpreted as arising from a two step process in which laser photons are backscattered to GeV energies by the electron beam followed by a collision between the high energy photon and several laser photons to produce an electron-positron pair.

The creation of superthermal electron-positron pair is a relativistic effect. Both becouse the conversion of mass Û energy and the relativistic energies of created particle-antiparticle pairs. The natural frame to analyse the relativistic gases of particles is the quantum heat transfer equation (QHT) .

2  Ranges of interactions and heaton energies for quark, electron and nucleon gases

The GeV energy of laser photons emitted in SLAC experiment are precursors of a new field of interdisciplinary applications of laser femtosecond beams. This superenergetic photons can in principle create not only electron and nucleon fermionic gases but also the free quark-gluon gas (if it exist!).

In paper  the quantum heat transport equation (QHT) was formulated. For electron and nucleon gases the QHT has the form:
for electrons

te 2 Te
t2
 + Te
t
 = (h/2p)
me
 Ñ2Te
(2)
for nucleons

tN 2 TN
t2
 + TN
t
 = (h/2p)
m
 Ñ2TN
(3)
In Eqs (2) and (3) me and m are the masses of electron and nucleon respectively and:

te = (h/2p)
mea2 c2
 ,       tN = (h/2p)
m(as)2c2
(4)
where te and tN are the relaxation times for electrons and nucleons respectively. The constants a = e2/(h/2p) c, as = mp/m (mp denotes the p meson mass), are the fine structure constants for electromagnetic and strong interactions.

As was shown in paper  static spherically symmetric solutions of equations (2) and (3) potentials has the form:

Ve(r)
=
- ge
r
 e-[r/( Re)],        ge = a(h/2p) c
(5)
VN(r)
=
- gN
r
 e-[r/( RN)],        gN = as(h/2p) c
(6)
where the ranges of electromagnetic interaction (in solids) and strong interaction in nucleus equal:

Re
=
2(h/2p)
meac
 ,
(7)
RN
=
2(h/2p)
mas c
(8)
The potentials Ve(r),  VN(r) are the Debye-Hückl potential and Yukawa potential respectively .

It is quite natural to pursue the study of the thermal excitation to the subnucleon level, i. e. quark matter. Analogously as for electron and nucleon gases for quark gas the QHT has the form:

1
c2
 2 Tq
t2
 + 1
c2t
 Tq
t
 = (aqs)2
3
 Ñ2 Tq
(9)
with aqs the fine structure constant for strong quark-quark interaction. In paper  aqs was calculated, aqs = 1. The heaton energy  for quark gas can be defined as:

Eqh = mq
3
 (aqs)2 c2
(10)
where mq denotes the average quark mass, mq = 417 MeV . With formmula (10) the heaton energy for quark gas is equal:

Eqh @ 139  MeV = mp
(11)
It occurs that when we attempt to ``melt'' the nucleons in order to obtain the free quark gas, the energy of the heaton is equal to the p - meson mass. This is the thermodynamics presentation for the quark confinement. Moreover we conclude that only from hyperbolic quantum heat transport equation we obtain finite mass for particle which mediates the strong interaction. For parabolic heat transport equation tN®0, i. e. (formula 4):

tN = (h/2p)
m(as)2 c2
 = (h/2p) m
mp2 c2
 ®0
(12)
hence mp® ¥. Analogously from Fourier equation one can concludes that due to the fact that vh®¥, all interactions must have zero range as from formulae (7), (8)

R e, N, q = 2(h/2p)
mvhe, N, q
 ®0
when vh®¥. In Table 1 the results for calculations of the ranges of interactions and heaton energies for electron, nucleon and quark gases are presented. From the inspection of the Table 1 we conclude that the Fourier equation can not be applied to study of the thermal processes on the atomic, nuclear and quark scales.

3  Conclusions

In this paper the validity of the quantum heat transport equation (QHT) for the description of the thermal processes on the atomic, nuclear and quark scales is discussed. It was shown that the static solution of the QHT gives the correct ranges and shapes of electromagnetic and strong interactions. When QHT is applied to quark gas the heaton energy is of the order of p-meson mass. This is the manifestation of the quark confinement, well described by quantum chromodynamics . The parabolic heat transport equation (when t® 0,  vh® ¥) gives the unphysical values for ranges and heaton energies (Table 1) calculated for electron, nucleon and quark gases.


Range [m]Heaton energy [eV]
 particlesQHTFourierQHTFourier
 quarks10-1601.39  108¥
 electrons10-1009¥
 nucleons10-1507  106¥

References

J. C. Diels, W. Rudolph, Ultrashort Laser Pulse Phenomena, Academic 1996
M. D. Perry and G. Mourou, Science 264, (1994) 917
E. P. Liang et al., Phys. Rev. Lett. 81 (1998) 4887
R. Svenson et al., Astrophys. J. 283 (1984) 842
D. L. Burke et al., Phys. Rev. Lett. 79 (1997) 1626
M. Kozlowski, J. Marciak-Kozlowska, Lasers in Engineering 7 (1998) 81
M. Kozlowski, J. Marciak-Kozlowska, Hadronic Journal 20 (1997) 289
B. Povh, K. Rith, Ch. Scholz, F. Zetsche, Particles and nuclei, Springer 1995

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