The Fingerprints of Periodic Electric Fields on Line Shapes Emitted in Plasmas
Round 1
Reviewer 1 Report
The manuscript "The fingerprints of periodic electric fields on line shapes emitted in plasmas" by Ibtissem Hannachi and Roland Stamm presents calculation of line shapes of hydrogen plasma. The authors solve Schrödinger equation of a hydrogen atom affected by electron collisions (employing binary collision approximation), electric fields from (static or dynamic) neighboring ions in the dipole approximation, and external oscillating electric field, also in the dipole approximation. Averaging over many initial conditions, the authors calculate emitted line shapes for the Lyman-alpha, Lyman-beta, Balmer-alpha, and Balmer-beta transitions.
Unfortunately, the manuscript lacks comparison with experiments and even with calculations by other groups, which (i) prevents judging if the authors approximations and calculations are valid and (ii) makes it unclear what is the novelty here, namely, what scientific problem the authors solved. As the authors correctly pointed out in the introduction, "Line shape changes due to oscillating electric fields have been studied since the beginning of quantum mechanics," thus, comparison with the previous works is a must.
Further, the results are not presented in a clear way. I summarize my suggestions in the list below.
1. As the authors correctly write (lines 39-41), "The problem with most of the line shape calculations is that they are based on numerous approximations, since Stark broadening is a complex problem involving plasma and quantum physics." This is fully correct for the presented calculations as well. Comparison with experiments and calculations by other groups, desirably using different approximations, must be presented to justify now questionable correctness of the results. These comparisons can also demonstrate how the presented calculations are better than the previous ones.
2. The authors write (lines 159-162): "If a fixed direction of the oscillating field is assumed, we take the z axis along it, and the line shape becomes dependent on the angle θ between the line of sight and the z axis. The line shape can be expressed as:" followed by Eq. (8) for the angle-dependent line shape. However, this dependence is not shown in the Results, and moreover, it is not clear what angles are assumed in all the results presented.
3. The equation for the unperturbed Hamiltonian (line 113) should be provided.
4. In many places text descriptions are used instead of formulas, which is probably Ok for press releases or popular magazines, but not for a scientific journal. Text cannot replace equations. The text descriptions may be kept, of course, if the corresponding formulas are added. For example:
"electronic collision time t_ce defined as the ratio of mean interparticle distance r_0 to the mean electron velocity v_e." -> "electronic collision time t_ce defined as the ratio of mean interparticle distance r_0 to the mean electron velocity v_e: t_ce = r_0/v_e."
"y_min the square of the ratio of the electronic Weisskopf radius ro_wi to the Debye length" ->"y_min the square of the ratio of the electronic Weisskopf radius ro_wi to the Debye length, y_min = (ro_wi/lam_D)^2."
and in many other places
5. Similarly, sentences like "something is much larger than something_else" would be nice to write in the form "something>>something_else," or combine texts and inequalities.
6. In the present version, the amplitude of the oscillating electric field, E_m, is given in terms of E_0 only. The value in V/m units is also necessary. By the way, there are also several sentences describing relations between E_w, E_m, and E_0, and E_0 itself, all by plain text without formulas. It would be easier for readers if formulas were added to the description.
7. Figs. 2-7: the horizontal axes labels, w/w_p, look wrong. It seems the correct labels would be (w-w_nm)/w_p, where w_nm is the central frequency of the corresponding transition. This (or similar correct label) should be described. Also, what is shown in Figs. 2,4, are not the "Central part", contrary to the caption, but inly w>w_nm part. If the lines are symmetric, the assumed symmetry should be explicitly stated in the figure captions, otherwise the w
8. The plasma frequency values (w_p) corresponding to the shown examples should be provided for convenience of the readers in the units of Hz or THz or PHz (or, perhaps, eV). By the way, the frequency of transitions themselves in the same units as w_p would be useful as well, just for the comparison.
Author Response
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Reviewer 2 Report
The manuscript deals with the results of a computer simulation model for Stark lines shapes in the presence of periodic electric fields. It is supposed that the electric field is of the order or larger that the mean plasma microfield. Effects of ion dynamics , electron broadening, and the oscillating electric field are taken into account. The approach adopted is computational simulations combining a simulation of the motion of charged plasma particles with an integration of the emitter Schrödinger equation for the case of the first Lyman and Balmer lines of hydrogen. Being published the results will be useful for the plasma physics community dealing with dense plasmas.
To my mind the paper can be accepted after some reorganization of References. The only 4 of the total 27 papers have been published in recent years.
Author Response
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Reviewer 3 Report
Dear Authors, Editor,
I appreciate the clarity and nice presentation of a challenging topic. However, I have a few comments that I would like the authors to attend. In random order:
1) Periodic electric fields necessarily would include "resonant" electric fields. For example, coherent electric field commensurate with one of the atomic resonances. One would need to include ac Stark broadening. Please comments and/or state that the work does not address resonant fields.
2) Figure 1 - please enhance the display for 10 E_m because the temporal undulations are difficult to demarcate (possibly use an inset).
3) Figure 7 (and also other figures) shows a relatively broad undulation for 3 E_m. Please clarify and/or emphasize in the text that there is a line narrowing due to the periodic field.
3) Also Figure 7: For higher electron density (say 10 to 100 times higher than in Fig. 7) the hydrogen beta line becomes asymmetric, but your graph implies symmetry. Please include a comment regarding possible asymmetry.
4) Figure 6: Please clarify the results for different Omega, perhaps use sub-figures.
5) Your work on oscillations, fig. plasmons, uses a classical approach (actually semi-classical). For resonant interactions, one can show that "semi-classical" is OK for coherent (viz. laser) fields. It would be helpful for you to comment on quantum mechanical inclusion of plasmons.
6) Do you have some references on experimental verification?
7) It may also be of interest to see computation results for H-alpha and for electron densities of the order of 10^18/cc, and for H-beta and for electron densities of the order of 10^17/cc. Can you include comments.
Respectfully,
Only minor edits needed.
Author Response
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Reviewer 4 Report
This is an interesting paper that should be published. It should be improved on the clarity front and I will offer some suggestions. Basically the ‘fingerprints’ are
a) The sattelites (which are not obvious if oscillatory field amplitudes are random) and
b) The ‘slower decorrelation’, i.e. smaller widths
And I think these should be made clearer at the very start.
In more detail:
-First page, line 37 “many theoretical studies” should read “main theoretical approaches”
-The last sentence of page 1 is too long and cumbersome. Are the authors trying to say “We limit our interest in this paper to hydrogen atoms, and neglect a) quenching collisions (i.e. collisions which cause transitions between states of different quantum numbers and b) nondipole interactions. These are thought to be the main source of inaccuracy of the calculations[9]” ?
-Second page, Section 2, lines 57-58. “decorrelation time” is most usually called “memory loss time”. It’s ok to call it decorrelation time, but just to avoid the reader having to wonder, it would be best to write “decorrelation (memory loss) time”.
-Second page, lines 65-67. The quasistatic Weisskopf radius criterion mentioned is not quite correct (see for example Seidel’s 1981 Spectral Line Shapes talk where it is explained that this assumes that strong collisions are static) and if applied in a plasma without electrons it would predict that line with a central component could become quasistatic at high enough densities, which is not true. The authors may elaborate on this criterion, but probably it is best to skip it altogether because the quasistatic approximation is not invoked.
-Third page, line 98 “coupled plasma conditions”. I assume the authors mean “strongly coupled plasma conditions”. If so, this should be added.
-Fifth page, line 177-178: “The DAF obtained with E_w=0 is not affected by a periodic field, but shows” . Isn’t it obvious that if E_w =0 there is no periodic field to affect anything in the first place? If so, then it would be best to write “The DAF for E_w=0 shows….”
-Fifth page, last paragraph: This is important and in tune with previous works done (e.g. ref 8 and JQSRT 71, 139(2001). The main point is that ion dynamic (or in general any broadening effect) is reduced by the oscillatory field. This of course is also relevant in principle for the electron broadening operator to the extent that it is not dominated by ion broadening. It might also be a good idea to point out that although ion dynamics is expected to be unimportant at the wings, (hence the 2nd and 3rd sattelites), this applies to the wings of each component, as the line has effectively been renormalized by the oscillatory field.
-Seventh page, lines 222-224. “The difference seen between the two calculations for the third and subsequent satellites is a measure of the statistical noise which increases as onE moves towardS the line wing”
Apart form the grammatic corrections in capital, are the authors talking about the noise of the simulation? If so, they should either elaborate or give a reference.
-eight page, line 234 “factor two” should read “factor OF two”
-I am also not sure on the explanations about the resonance given in lines 238-246. As shown by Blokhintsev, the central intensity is proportional to the square of a Bessel function Jo. This is an oscillatory function, which can and does become 0 for specific values of E_w/Omega_p. What is true is that the E_w=0 gives a maximum, but it is not true in general that the higher Omega_p, the higher the intensity of the central satellite (although always < that the no field case). So the authors should either explain and document this assertion, or withdraw this explanation
Minor english corrections or typos required
Author Response
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Round 2
Reviewer 4 Report
I think the revised version is fine and will be a useful contribution to the field.
