diploe emits the electromagnetic wave with its intensity dependence on angle
proportional to:
I /
dj
dt
2
cos
2
θ
ð2:3:16Þ
where θ is the angle of the propagation direction from the horizontal axis. Time
derivative of the current stems from RHS of (2.2.10) and is proportional to the square
of the charge acceleration. This dependence represents Larmor emission of
radiation.
The fact that the oscillating current generates electromagnetic field means that
impinging electromagnetic field is scattered by free electrons in plasma. This
scattering is Thomson scattering. The cross section of Thomson scattering σ T
doesn’t depend on parameters of the electromagnetic field and constant:
σ T ¼
8
3
πr
2
e ¼ 6:65 Â 10
À25 cm
2
ð2:3:17Þ
where r e is the electron classical radius defined as:
e
2
4πε 0 r e
¼ mc
2
) r e ¼
e
2
4πε 0 mc 2
ð2:3:18Þ
The first relation above means that the electron-binding energy mc
2 can confine
against Coulomb repulsion at the radius of r e . It is noted that the electron density in
solid metal is roughly of the order of 10
22–24 cm
À3, and the scattering fraction of mm
size sample is weak. With use of precise measurements of the scattered photons of
cohenerent X-ray, say XFEL (X-ray- free electron lasers), from a dynamically
compressed sample, it is possible to measure the column density [product of density
and length], and the electron temperature from the spread of spectrum by Doppler
shifts due to thermal electrons.
Since Tomson scattering gives a fraction of the momentum of the electromagnetic
field (ħk), a very bright light source repels the falling electron cloud to the source.
Such situation may happen in the case of the birth of very massive stars like
100 times solar mass. Once the electrons obtain photon momentums, accompanying
protons are also dragged by the ambipolar electric field generated by electrons.
Assuming hydrogen plasmas are falling to the surface of a baby star with mass M
and its total light energy flux L (luminosity), the maximum mass of the star is limited
by the following force balance relation:
σ T
L
c4πR
2
¼ G
Mm p
R
2
ð2:3:19Þ
where R is the radius of the star, and G and m p are the gravitational constant and the
mass of a proton. In general, the luminosity L has strong dependence on the mass M
2.3 Electron Current Induced by Laser Fields
49
proportional to:
I /
dj
dt
2
cos
2
θ
ð2:3:16Þ
where θ is the angle of the propagation direction from the horizontal axis. Time
derivative of the current stems from RHS of (2.2.10) and is proportional to the square
of the charge acceleration. This dependence represents Larmor emission of
radiation.
The fact that the oscillating current generates electromagnetic field means that
impinging electromagnetic field is scattered by free electrons in plasma. This
scattering is Thomson scattering. The cross section of Thomson scattering σ T
doesn’t depend on parameters of the electromagnetic field and constant:
σ T ¼
8
3
πr
2
e ¼ 6:65 Â 10
À25 cm
2
ð2:3:17Þ
where r e is the electron classical radius defined as:
e
2
4πε 0 r e
¼ mc
2
) r e ¼
e
2
4πε 0 mc 2
ð2:3:18Þ
The first relation above means that the electron-binding energy mc
2 can confine
against Coulomb repulsion at the radius of r e . It is noted that the electron density in
solid metal is roughly of the order of 10
22–24 cm
À3, and the scattering fraction of mm
size sample is weak. With use of precise measurements of the scattered photons of
cohenerent X-ray, say XFEL (X-ray- free electron lasers), from a dynamically
compressed sample, it is possible to measure the column density [product of density
and length], and the electron temperature from the spread of spectrum by Doppler
shifts due to thermal electrons.
Since Tomson scattering gives a fraction of the momentum of the electromagnetic
field (ħk), a very bright light source repels the falling electron cloud to the source.
Such situation may happen in the case of the birth of very massive stars like
100 times solar mass. Once the electrons obtain photon momentums, accompanying
protons are also dragged by the ambipolar electric field generated by electrons.
Assuming hydrogen plasmas are falling to the surface of a baby star with mass M
and its total light energy flux L (luminosity), the maximum mass of the star is limited
by the following force balance relation:
σ T
L
c4πR
2
¼ G
Mm p
R
2
ð2:3:19Þ
where R is the radius of the star, and G and m p are the gravitational constant and the
mass of a proton. In general, the luminosity L has strong dependence on the mass M
2.3 Electron Current Induced by Laser Fields
49