21 May 2004: D. Cohen
My comments in italics.

Subject:
Re: two questions re: PHP manuscript
From: Otto Landen <landen1@llnl.gov>
Date: Wed, 18 Feb 2004 10:01:04 -0800
To: dcohen1@swarthmore.edu

> David,

Paper nicely written, and by reading, I have been forced to learn things I was vague on.  I especially like idea of disk outside halfraum and explanation of hohlraum vs halfraum Dante Tr.  My comments by Page number:

1) First sentence should say single (also known as halfraums) and double-ended hohlraums in ICF and High Energy Density Physics (reference Lindl and Rosen paper above)

OK; wording in abstract still seems a little awkward to me.  Both papers are now referenced in the abstract, and also in the body of the paper. 

2) Give % LEH size here and elsewhere. Also, beam focus conditions.

Done and done. 

Explain that VISRAD assumes Lambertian optically thick surface source.  

OK; two paragraphs describing VISRAD has now been composed, and appear near the beginning of sec. II. 

This does ignore fact that there is Tr gradient in wall which means re-emission Tr will increase as view wall at more and more oblique angles. This is least serious at late times (high albedo) when Marshak wave has penetrated ‰ 1/(1-albedo) mfps.  Rough estimate of effect (which I first heard from M. Rosen) given by assuming flux drops linearly into wall over 1/(1-albedo) mfps and ray at angle beta to wall sees into average depth mfpsin(beta):

T(beta)/T(normal) = [(1-(1-albedo)sin(beta))/(1-(1-albedo)]^0.25 where beta is angle from wall surface.  This gives T(45°)/T(normal) = 1.02 for albedo = 0.75.

Very interesting.  Makes sense.  I now mention (the neglect of) this effect.  Also other approximations and limitations of the view-factor approach.  I hope it's not too negative.  

However, after reading the Rosen paper (1996, Phys. Plasmas), which I liked, I don’t see this effect mentioned.  Is it described in some other paper of his? (As of now, the effect’s discussion is un-referenced.) 

I guess you mean XCE accounts for plasma motion by implicitly assuming energy lost to hydro?

Yes.  I've slightly modified the wording, and hope it's clearer now. 

Note: I’ve added a paragraph to sec. II in which I do an analytic power balance calculation, and compare the results to our view-factor calculation.  The Tr from the analytic calculation falls in between the DANTE Tr and the sample Tr from the view factor calculation, which all seems to make sense.  Please let me know if this discussion could be improved, or perhaps moved to a different location in that section. 

This calculation is detailed at: http://hven.swarthmore.edu/~cohen/hohlraum/power_balance_notes.jpg

More scientifically curious is the relatively low XCE, compared to values usually seen in the literature (0.75 to 0.8; see for example Suter’s paper referenced here, or Rick Olson’s 2003 RSI paper).  I note that in the Decker et al. experiments, a value of 0.55 seems to work fine (same for our NLUF OMEGA exps).  Any idea why XCE values can, or might, vary?  Is there a good physical understanding of where these XCE values come from?  

Joe and I have been talking about where our value of XCE=0.55 comes from.  We did NOT tune it to match the Decker experiments, rather it was handed down to use through “lore” we seem to recall by Glenn Magelssen.  

3)  When explaining Fig. 4 trends, the size of LEH lip should be mentioned as does factor into Dante view as pointing changes.

Agreed.  I now also foreshadow the small study and discussion of varying the LEH size in the halfraum simulations (sec. IV). 

I would combine top 2 Figs. 2 and make fonts bigger.

Done. 

4) Reference Back, PoP 7 (2000) 2126 for halfraums.  

OK, though this paper is HEDP focused, not ICF focused.  Any other suggestions?  I did a literature search and found 346 papers with the word “hohlraum” in their abstracts, but none (!) with the word “halfraum” and only one with the term “half hohlraum”. 

Also, I enclose Suter paper on hohlraum drive worth referencing.

Already had it and had referenced it in another context. 

I would mention that finding that Tr on sample does not depend on sample orientation or position is why symmetry can be achieved in cylindrical hohlraums and why ICF is attempted in cylindrical hohlraums.

Of course.  I've simplified this discussion and pointed out, as you say, that this lack of sample orientation dependence on drive temperature is by design. 

Discussion on LEH vs wall-facing samples at end of penultimate paragraph seems contradictory.  Which has harder spectrum?

LEH-facing one has the harder spectrum.  It was reversed in one mention in the text.  I believe it's all consistent and corrected now. 

5) Specify disk is also made of Au.

Done. 

It would be worth going through simple power balance model of why adding the divider wall only drops sample Tr by 1%.  Offhand, I would have expected more since assuming 50% of energy lost to walls and increase wall area by 20% should increase losses by 10% which is >2% in Tr.

Good intuition.  Turns out that the sample temperature was 190, not 188 (just a typo when copying into the LaTeX from my notes).  That's corrected now. 

For explanation on higher Dante Tr for hohlraum, I would be more specific and say that Dante also sees laser hot spot emission from beams entering the opposite LEH of the hohlraum.  This is to distinguish from case where low angle beams can cross hohlraum midplane before striking wall.  In that case, Dante views of hohlraums and halfraums could be fairly similar as a low angle beam that would cross a hohlraum mid-plane would illuminate the divider disk in a halfraum visible by Dante (could actually make halfraum appear hotter as low angle beams would hit divider more head-on than hohlraum wall).   I would add this discussion in here as very relevant to NIF where 1/3 of beams are low angle and cross.

OK, I've clarified this and added a mention of the NIF-relevance. 

6) Role of LEH lip size should be included.

Yes, one new series of simulations at the end of Sec. IV...

I am puzzled why you say solid angle of hot spots decreases as move closer to back-wall sample?  

I didn't think about it carefully.  The angle becomes more oblique as the spots move in, but the distance also gets smaller and the projection effect of the spot shape diminishes.  

Fig. 8 shows spots  looking bigger as move closer to sample, and I calculate solid angle varying roughly as 1/z^2 where z is axial distance between wall and spots.  I am assuming we are considering a sample point element which does not weight radiation flux arriving on it by angle which it arrives? (This is not so when considering ablation pressure on finite sized sample with finite gradient where arrival angle of x-rays does matter).

OK, I’ve looked into this further, and have done a little analysis. See notes and a plot at: 

http://hven.swarthmore.edu/~cohen/hohlraum/spot_flux_notes.jpg
and
http://hven.swarthmore.edu/~cohen/hohlraum/spot_flux.jpg

It seems there will always be a spot position that maximizes the flux onto the sample, with smaller fluxes for both deeper and shallower pointings (flux, not solid angle, is what’s relevant; I was sloppy with the wording in the earlier version of the manuscript). 

I would further explain similarity in Tr at low albedo by fact that distinction between Dante seeing walls and sample seeing walls and LEH is lost as both walls and LEH are much colder relative to laser spots and hence unimportant contributors of drive.

Yes, well said.  I've added a sentence explaining this. 

7) In section V, make clear that pointing is kept fixed wrt to LEH.  

Right.  Done.

This brings up suggestion for another set of simulations I have often wondered about:  How does Tr vary as pointing relative to end package kept fixed but halfraum length varied (to the extent possible while avoiding clipping of beams at LEH lip)?  My guess is that Tr on sample will go up as halfraum lengthened (which, if true, is interesting as goes against simple-minded power balance formula which says more wall area decreases Tr).

I've done this simulation, and the sample temperature is virtually unchanged as the halfraum lengthens.  See new figures and text. 

8) Exterior/interior sentence grammar problem.

Thanks for catching this.  It's shortened and clarified now. 

9) Sentence " In standard halfraum...", I would say temperatures are closer and talk about a 5 eV difference at 200 eV rather than disagreement, since when accounted for, no discrepancy.

I think the emphasis is already on the good agreement (for the halfraum).  But I've made minor changes to the wording to bring this out more. 

By the way, there are a couple of places where I note that a specific temperature difference corresponds to a specific flux ratio.  Let me know if you see other places where such a reminder would be useful. 

...because Dante sees some of the hot spots from laser beams entering the opposite LEH of the hohlraum.

Got it. 

OK, that’s it for the specific changes and comments.  In my mind, the big question still remaining is the issue of the XCE and what its value might reasonably be assumed to be (and why it seems to vary from one experiment to the next).  I would point out, however, that heating scales linearly with XCE, so the basic results in the paper (relative temperature differences between DANTE and sample Tr, for example) do not depend on the specific value of XCE that’s assumed. 

I wonder if the actual value of the beam powers in the Decker et al. experiments might have been significantly lower than 500 TW (allowing, then, for a higher XCE to give the same Prad).  Is it possible to find out the beam powers from those experiments? 

I’d also note that the capsule vs. DANTE temperature differences, though they weren’t commented on in Decker et al., are apparent in Fig. 4 of that paper. Should we mention this in the manuscript? 

Minor additional comments/questions: 

-	Should “cone” be capitalized, as in “Cone 2 beams”? 
-	Is the viewing angle dependence on emitted flux via wall temperature gradient effects discussed somewhere in the literature (by Rosen, or by someone else)? 
-	Should we mention the focal ratio of the OMEGA beams?
-	Are there additional places in the manuscript where we might include an analytic power balance calculation to compare to the numerical view factor results (aside from the one place in Sec. II where I’ve included such an analysis)?