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Submitted on 1 Jan 1979
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SELF-GENERATED MAGNETIC FIELDS AND HARMONIC EMISSION
T. Boyd, G. Gardner, G. Humphreys-Jones
To cite this version:
T. Boyd, G. Gardner, G. Humphreys-Jones. SELF-GENERATED MAGNETIC FIELDS AND HARMONIC EMISSION. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-551-C7-552.
�10.1051/jphyscol:19797266�. �jpa-00219252�
JOURNAL DE PHYSIQUE CoZZoque C7, suppZdment au n07, Tome 40, JuiZZet 2979, page C7- 551
SELF-GENERATED MAGNETIC FIELDS AND HARMONIC EMISSION
T.J.M. Boyd, G.A. Gardner and G.J. ~umphreys-Jones.
~ n i v e r s i t y of Wales, U. C. N. W., Bangor, WaZes.
Recent observations of self-generated magnetic f i e l d s i n plane target experiments [11 with high powered lasers have prompted us to look again a t harmonic emission from magnetized plasmas. I t is well known from the work of Fidone and h i s collab- orators C 2,31 that second h a m n i c generation i n Tokamak plasmas has not only been observed but has proved t o be a useful magnetic f i e l d diagnostic.
In the experiments by Raven and his co-workers, megagauss f i e l d s were measured i n the quarter-
c r i t i c a l density region, from which one might expect that magnetic f i e l d strengths close t o c r i t i c a l density would be very large indeed
-
parhaps as big as lOMG
-
though no measurements have yet been made in t h i s region. In the presence of such strong magnetic f i e l d s i t has been shown recently t h a t significant absorption of normal1 incident l a s e r l i g h t i s possible, t o g e t k rh a m n i c generation C4,SI. In t h i s paper we
w d
report a theoretical study of h a m n i c generation together with results obtained from numerical experiments using a l a - D code, EMPIRE. The computer experiments, i n addition t o providing information on h a m n i c emission, also indicate that a strong quasi-static magnetic f i e l d i s gener- ated i n the neighbourhood of the resonance region.
This f i e l d has been detected i n simulations carried out independently C61.
The configuration examined i n t h i s work i s the following. An electromagnetic wave propagates along Ox and i s n o m d l y incident on a plasma density ramp. The e l e c t r i c f i e l d of the incident wave i s aligned along Oy
.
We s h a l l suppose that a magnetic f i e l dBo
i s applied along Oz.
A sthe wave propagates into the plasma, the Ey f i e l d induces electron oscillations along by and the resultant y x
B
force effectively produces particle motion i n the direction of propagation.Thus by charge separation along the density gradient, an e l e c t r o s t a t i c f i e l d component Ex is produced. This is of course just the extraordin- ary made i n the plasma. The i n t e r e s t i n t h i s mode stems from the f a c t that NR
,
the density a t- -
which the wave resonates a t the local upper hybrid frequency, and NC
,
the cut-off density, are related by NC = ~ $ 1-
Qe/wol,
where Qe is the electron cyclotron frequency and wo,
thefrequency of the incident wave. Consequently i f 52 << wo
,
as i s certainly the case i n Nd l a s e re.
plasmas, then Nc = NR
.
We then have a -situation analogous t o t h a t of obliquely incident radiation i n unmagnetized plasmas. The d i f f e r e n e between the two cases i s that in the l a t t e r the separation between the cut-off and resonant dens- i t i e s is governed by the angle of incidence of the wave, whereas i n the magnetized plasma considered
here, t h i s separation i s governed effectively by the strength of the magnetic f i e l d . Thus resorant absorption of a normally incident wave i s made possible by the magnetic f i e l d and has been exam- ined both theoretically and by computer sirrmla- tions
.
This resonance takes the form of a plasma disturbance which produces a large localized oscillating electrostatic field. The rapid spatial variation of t h i s f i e l d produces anhamnic oscillations of the electrons, due t o t h e i r being
subjected to varying e l e c t r i c f i e l d strengths over t h e i r excursion lengths. This electron behaviour may be represented as a series of Fourier modes a t wo,2wo,%
...
and these modes then provide a current density source with components a t 2 w o , h o... .
The particular modes responsible f o r the generation of the 2wo current density are the wo and 2w0 electron oscillations. The former beats with the oscillating electron number density N(wo) to produce a componenteN(wo)Ve(wo) while the l a t t e r conbines with the unperturbed number density to give a term eNoVe(2wo)
.
Hence as a direct r e s u l t of t h e resonant mechanism a current density J(2wo) is produced which, i n turn, provides the source of second harmonic emission.Fig, 1
8
-
Theory ; X-
Computation.Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797266
To find the relation between the power i n the incident wave and that re-emitted as second h a m n - i c
,
we have t o determine the current density. This is then treated as "free" current and is used as a source term i n the second harmonic wave equation.This relationship has been evaluated and Fig. 1 shows a comparison between the theoretical r e s u l t s and those obtained from computer simulations. The parameter on the abscissa. i s the r a t i o of the distance between cut-off and resonant layers and the scale of variation of the electromagnetic wave near cut-off; ko = wo/c and L is the plasm scale length, i.;. the distance between the c r i t i c a l density and t h e boundary. While there is some discrepancy between the theoretical results and those from the computer experiment, the overall agreement i s quite good.
Fig. 2
The dominant component of the resonantly induced current density l i e s across the density gradient, i .e. along Oy
.
This component is responsible for inducing a magnetic f i e l d along Oz.
This f i e l d i s quasi-static and, in the cold plasma limit, i s resericted s p a t i a l l y t o the plasm resonant region. However warm plasma theory predicts t h a t the magnetic f i e l d w i l l extend into the over-dense region, and t h i s is observed i n the computer simulations. Fig. 2 shows a plot, from our simulations, of the time-averaged magnetic field. The direction of the f i e l d reverses inside the resonant region which extends over 2 A . Also the f i e l d extends into the over-dense plasm.We have also examined the influence of the magnetic f i e l d effects on the h a m n i c l i n e profiles. Fig. 3, taken from a run of our
11-D
f u l l y electromagnetic code shows the l i n e structure present on the second h a m n i c emission spectrum.
The frequency s h i f t of the f i r s t side band, relat- ive t o the l i n e centre, can be seen. This is strongly dependent on magnetic f i e l d intensity.
Fig. 3
excitation of Bernstein modes. The sirrmlations also indicate t h a t strong quasi-static.magnetic f i e l d s are generated i n the neighbourhood of the c r i t i c a l density.
References
1. A. Raven, 0. W i l l i , andP.T. Rumsby, Phys.
Rev. Lett.
41,
554 (1978).2. R. Cano, I. Fidone and M.J. Schwartz, Phys.
Rev. Lett. 27, 783 (1971).
3. T.J.M. Boyd and I. Fidone, Phys. Fluids
16,
427 (1973)
.
4. 1V.L. Kroer and K. Estabrcok, Phys. Fluids 20, 1688 (1977).
5. W. Woo, K. Estabrook and J.S. De Groot, Phys.
Rev. Lett. 40, 1094 (1978),
6 . W. Woo and J.S. De Groot, Phys. Fluids Zl,
2072, (1978)
.
In summary we have shown t h a t significant h a m n i c emission may be produced in l a s e r
produced plasmas with strong magnetic fields. The harmonics show structure consistent with the
