(b) is nothing without the collisional absorption, and it is also called inverse
Bremsstrahlung (IB) absorption.
If the system is optically thick plasma such as inside the sun, the photons
generated by Bremsstrahlung process are soon absorbed by IB process. In such
optically thick system, it is well-known the radiation is in Planckian energy
distribution. It is said that in such LTE system, detail balance of each elementally
process is established. Then, the photon distribution is Planckian distribution for a
given temperature. Planckian distribution as a function of photon frequency is in the
form:
f P ν
ð Þ ¼
8πh
c 3 ν
3
1
e hν=T À 1
dν
ð2:7:1Þ
In the laser absorption case, the photon distribution at laser frequency is much higher
than (2.7.1) for plasma temperature, and the IB absorption is much larger than the
Bremsstrahlung emission process.
Note that (2.7.1) has a form of (1.2.2) and g is proportional ν
3 and f is given in the
term including exponential function in (2.7.1). If the density of state does not
decrease so fast as ν, the distribution diverges near ε (¼hν) ¼ 0. This is BoseEinstein condensation. However, the density of state of photon quanta is small near
ε ¼ 0, Planckian distribution has a peak near hν ¼ 2.8 T.
References
1. T. Makabe, Z. Petrovic, Plasma Electronics (Taylor & Francis, 2006)
2. C.J. Joachain, N.J. Kylstra, R.M. Potvliege, Atoms in Intense Lasers (Cambridge University
Press, 2012). M. Protopapas, C. H. Keitel and PO. L. Knight, Rep. Prog. Phys. 60, 389 (1997).
C. J. Joachain, EPL, 108, 44001 (2014)
3. L.D. Landau, E.M. Lifshitz, Quantum Mechanics (Elsevier Science, 2003)
4. K. Mishima et al., Phys. Rev. A 66, 033401 (2002)
5. S. Augst et al., J. Opt. Soc. Am. B 8, 858 (1991)
6. S. Augst et al., Phys. Rev. A 52, R917 (1995)
7. W.L. Kruer, The Physics of Laser Plasma Interactions (Addison-Wesley, New York, 1988)
8. R.S. Craxton et al., Phys Plasmas 22, 110501 (2015)
9. J. Dawson, C. Oberman, Phys. Fluids 5, 517 (1962). Phys. Fluids. 6, 394 (1963)
10. T.J.M. Boyd, J.J. Sanderson, The Physics of Plasmas (Cambridge University Press, 2003).
Chap. 10
80
2 Laser Absorption by Coulomb Collision
Bremsstrahlung (IB) absorption.
If the system is optically thick plasma such as inside the sun, the photons
generated by Bremsstrahlung process are soon absorbed by IB process. In such
optically thick system, it is well-known the radiation is in Planckian energy
distribution. It is said that in such LTE system, detail balance of each elementally
process is established. Then, the photon distribution is Planckian distribution for a
given temperature. Planckian distribution as a function of photon frequency is in the
form:
f P ν
ð Þ ¼
8πh
c 3 ν
3
1
e hν=T À 1
dν
ð2:7:1Þ
In the laser absorption case, the photon distribution at laser frequency is much higher
than (2.7.1) for plasma temperature, and the IB absorption is much larger than the
Bremsstrahlung emission process.
Note that (2.7.1) has a form of (1.2.2) and g is proportional ν
3 and f is given in the
term including exponential function in (2.7.1). If the density of state does not
decrease so fast as ν, the distribution diverges near ε (¼hν) ¼ 0. This is BoseEinstein condensation. However, the density of state of photon quanta is small near
ε ¼ 0, Planckian distribution has a peak near hν ¼ 2.8 T.
References
1. T. Makabe, Z. Petrovic, Plasma Electronics (Taylor & Francis, 2006)
2. C.J. Joachain, N.J. Kylstra, R.M. Potvliege, Atoms in Intense Lasers (Cambridge University
Press, 2012). M. Protopapas, C. H. Keitel and PO. L. Knight, Rep. Prog. Phys. 60, 389 (1997).
C. J. Joachain, EPL, 108, 44001 (2014)
3. L.D. Landau, E.M. Lifshitz, Quantum Mechanics (Elsevier Science, 2003)
4. K. Mishima et al., Phys. Rev. A 66, 033401 (2002)
5. S. Augst et al., J. Opt. Soc. Am. B 8, 858 (1991)
6. S. Augst et al., Phys. Rev. A 52, R917 (1995)
7. W.L. Kruer, The Physics of Laser Plasma Interactions (Addison-Wesley, New York, 1988)
8. R.S. Craxton et al., Phys Plasmas 22, 110501 (2015)
9. J. Dawson, C. Oberman, Phys. Fluids 5, 517 (1962). Phys. Fluids. 6, 394 (1963)
10. T.J.M. Boyd, J.J. Sanderson, The Physics of Plasmas (Cambridge University Press, 2003).
Chap. 10
80
2 Laser Absorption by Coulomb Collision