Injection system

[jgerity]

Edits to this section should be in paper_src/injection.md, discussion belongs here.

[LeeEdel]

I re-did the plasma calculations from scratch and tried to cross-check both with our values from class and with other approximations. I've added these to the repository under "USPAS_20160701_Plasma_Calculations_Updated.ipynb"

https://github.com/jgerity/uspas2016_project3/blob/master/USPAS_20160701_Plasma_Calculations_Updated.ipynb

--Note that I do end up with a different max accelerating field and thus different accelerating lengths required for each of our cases. I don't remember where we obtained the approximation for max accelerating field that we used (so if you do remember, please chime in). --I also don't have the expected output beam parameters other than energy. What do we need here?

[ghost]

Hi Auralee, I think we obtained the significantly higher accelerating fields because we were using powers of a_0 (as suggested by akash). so instead of sqrt(a_0)-which is the standard, we used a_0^(2/2).

And we were calculating E_max using: np.sqrt(n * a_02)/1e9 (E_max = plasma_parameters.addParameter("Max E field",np.sqrt(n * a_02)/1e9,"GV/cm").value())

As already mentioned in the course, I find that estimate VERY OPTIMISTIC.

[billyziege]

Hi Auralee and Marlene,

I actually think we used a_0 instead of a_0^1.5 or a_0^0.5. So not as bad as the 3/2 case, but a more optimistic estimate than the 1/2 case.

BTW. You can see this in the notebook:

E_max = plasma_parameters.addParameter("Max E field",np.sqrt(n * a_0**2)/1e9,"GV/cm").value()

Here, we have sqrt(a_0^2) = a_0. I know this is confusing, but it is because we tried 3/2, 2/2, and 1/2 and eventually settled on 2/2. Let me know if this isn't making sense.

Best,

Brandon

On Wed, Jul 13, 2016 at 8:16 AM, MarleneTurner notifications@github.com wrote:

Hi Auralee, I think we obtained the significantly higher accelerating fields because we were using powers of a_0 (as suggested by akash). so instead of sqrt(a_0)-which is the standard, we used a_0^(3/2).

And we were calculating E_max using: np.sqrt(n * a_0 _2)/1e9 (E_max = plasma_parameters.addParameter("Max E field",np.sqrt(n * a_0_2)/1e9,"GV/cm").value())

As already mentioned in the course, I find that estimate VERY OPTIMISTIC.

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[ghost]

Ah yes, you're absolutely right... Ill change my previous comment.

[Ossssip]

Hi everyone, Speaking of beam parameters, I believe that the beam charge was simply suggested by Andrei or by Aakash, and we did not estimate any energy spread or something like this as well.

I am sure that it is important to keep track which parameters were arbitrary selected and are truly independent (e.g. laser wavelength, laser pulse time, desired electron energy) and which were derived to fulfil certain conditions (a0 and plasma density to achieve enougth electron energy before laser dephasing/depletion, and almost everything else derived from these parameters).

I went through Brandon's file (call me lazy for not calculating everything from scratch) and it looks fine in general, but one thing I do not completely understand: we calculated laser power as np.pi * R_b * 2 * intensity * 100. * 2/1e12, i.e. R_b is taken here as the laser spot radius. Is it correct? This R_b value differs a lot from the spot size that Auralee used in her recalculations. I see the spot size on the whiteboard, but I have no records about calculating it.

[billyziege]

Hi Ossip,

In the write-up I did, I separated the "arbitrarily chosen" from the derived parameters. I agree we should do so in every section as you suggest.

The R_b value in the notebook is the same as in injection.md. That is, her spot size is an area, while our spot size is a radius. Convert the one to the other with spot_size = np.pi * R_b**2. I don't see your qualm. This is an order of magnitude estimate, by the way, so setting the spot radius to fraction of R_b will give a similar order of magnitude estimate.

Finally, looking at the injection.md table, though, the bubble size there is 38 um where we determined it to be 35 um in the notebook. The number in the table does look a lot like the spot_size number, maybe this similarity caused a typo? It's less than a 10% difference, though, so I am not asking for it to be changed, but I am just pointing that out in case...

Best,

Brandon

On Wed, Jul 13, 2016 at 11:23 AM, Ossssip notifications@github.com wrote:

Hi everyone, Speaking of beam parameters, I believe that the beam charge was simply suggested by Andrei or by Aakash, and we did not estimate any energy spread or something like this as well.

I am sure that it is important to keep track which parameters were arbitrary selected and are truly independent (e.g. laser wavelength, laser pulse time, desired electron energy) and which were derived to fulfil certain conditions (a0 and plasma density to achieve enougth electron energy before laser dephasing/depletion, and almost everything else derived from these parameters).

I went through Brandon's file (call me lazy for not calculating everything from scratch) and it looks fine in general, but one thing I do not completely understand: we calculated laser power as np.pi_R_b__2_intensity 100.*2/1e12, i.e. R_b is taken here as the laser spot radius. Is it correct? This R_b value differs a lot from the spot size that Auralee used in her recalculations. I see the spot size on the whiteboard, but I have no records about calculating it.

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[LeeEdel]

Hi All,

My main question is about where the np.sqrt(n)* a_0/1e9 comes from with a justification. Did we get any definitive source on this? Is it an accepted approximation by the community? The equation in the book gives us half the accelerating gradient, so I am inclined to think we should go with that unless we find a good reason for using the other approximation. I had sent around a few emails, reproduced below that articulates the questions better:

I put up a file on the repository that has the calculations I re-did and cross-checked for the laser/plasma parameters. It's under "USPAS_20160701_Plasma_Calculations_Updated.ipynb" here:

https://github.com/jgerity/uspas2016_project3/blob/master/USPAS_20160701_Plasma_Calculations_Updated.ipynb

I do have a few more questions:

1. The max accelerating gradient that I calculated is different than what we got in class. In class we used:

sqrt(n * a_0**2)/1e9 [GeV/cm]

but I don't remember where we obtained this expression.

I used the equation in Unifying Physics book margin on pg 106 instead and got about half the accelerating gradient.

I also looked at the E=(a0^(3/2))*m_e*c*w_p/e equation in the project handout but wasn't getting sensible numbers (e.g. hundreds of GeV/cm). It is possible though that I was making mistakes somewhere.

Which of these should we be using?

2. I haven't calculated anything for the output beam except for energy. Do we need anything else (like charge and energy spread) and if so where can we find a good approximation for this?

Related to this, I also have some concerns about the gas jet. With 2.4 cm and 7.2 cm needed to get 1 GeV and 3 GeV respectively, it looks like we might be outside of the length for a typical gas jet (I've only seen <1 cm, but that was with a cursory glance so let me know if you know of any gas jet experiments that used longer acceleration lengths). Also note that I'm still not sure about the approximation we used previously (see question 1) for the gradient, so the situation may not be as bad if we can trace where the approximation we used in the class calculations came from (it's not in the handout or the notes, and I think I may have just gotten it from a paper or something if it wasn't something that was written on the board).

Is it feasible to put multiple gas jets adjacent to one another along the line? I've not seen this done, so I am worried there might be something fundamental that limits one's ability to do this. Alternatively, is it sufficient to say that the design will require a novel gas chamber/jet to achieve these acceleration lengths? That puts a very large gap in our design.

I've put a very rough draft of the paragraph for the laser wakefield portion on github, and all of the calculations are in https://github.com/jgerity/uspas2016_project3/blob/master/USPAS_20160701_Plasma_Calculations_Updated.ipynb . However, I'm still not sure what needs to be done about output beam parameters other than energy (i.e. what approximations are accepted in the field for this regime, etc.).

[LeeEdel]

I did indeed just pull the spot size from the table rather than the original notebook from class, so I'll change that in the new injection notebook now.

[LeeEdel]

Also, note that I did not change the table at all, so those are not updated values. The injection notebook I linked to above has the most recent ones.

[LeeEdel]

And Ossip is correct about the beam charge. It was a suggested value that we did not calculate. This also relates to my question about how we approximate the output beam parameters other than energy. I have no intuition for what approximations are accepted in the field in this regime, and I haven't been able to find any general ones in the literature, so maybe Aakash can provide some guidance on this point.

In order to be consistent with the rest of the design, it is certainly something that should be addressed.

[LeeEdel]

For the laser calculations at least we have assumed: laser power (and adjusted slightly to get an a0 > 2 for self-guiding, as I recall?) laser wavelength laser pulse duration (and ensured it met the < pi/w_p condition after the fact along with our choice of n)

Then we calculated the rest of the laser parameters. Then we chose n to be below the critical density and to get acceptable dephasing and depletion lengths. Then we calculated our gradient and the acceleration length needed to get to 1 GeV and 3 GeV, and made adjustments as needed to the other chosen parameters.

For the ring as I recall, all of our beam parameters (energy, bunch charge) were assumed, not calculated.

Does this sound correct?

[LeeEdel]

But the major thing to figure out right now is what approximation for the accelerating gradient we should be using.

[billyziege]

Hi Auralee,

Since I wrote the notebook, you'd think I should be able to justify the acceleration gradient. I cannot. Quite truthfully, this was my first exposure to this type of physics, so I have absolutely no feel for what is correct.

You and Marlene are right to say that I pulled this directly from Aakash's suggestion, and I echo your hope that he will have some source to point us to.

Brandon

On Wed, Jul 13, 2016 at 3:01 PM, LeeEdel notifications@github.com wrote:

But the major thing to figure out right now is what approximation for the accelerating gradient we should be using.

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[LeeEdel]

Also note that the dephasing length I calculated is a factor of 10 different than what we had before, but I think it was just a mistake in the original notebook, perhaps?

[billyziege]

I don't see the difference in what is in injection.md and what is in the notebook. Are you comparing different sets of numbers or am I missing something?

On Wed, Jul 13, 2016 at 3:08 PM, LeeEdel notifications@github.com wrote:

Also note that the dephasing length I calculated is a factor of 10 different than what we had before. I'm looking into it.

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[LeeEdel]

The paragraph has the new values (to be clear, from USPAS_20160701_Plasma_Calculations_Updated.ipynb), but the table has the old ones from class. Some values are the same, but some aren't (e.g. max accelerating gradient, dephasing length). I'll put in a new table and retain the old one as well explicitly while we're still figuring it out.

[billyziege]

Aah. Thanks for the clarifications.

On Wed, Jul 13, 2016 at 3:15 PM, LeeEdel notifications@github.com wrote:

The paragraph has the new values (to be clear, from USPAS_20160701_Plasma_Calculations_Updated.ipynb), but the table has the old ones from class. Some values are the same, but some aren't (e.g. max accelerating gradient, dephasing length). I'll put in a new table and retain the old one as well explicitly while we're still figuring it out.

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[LeeEdel]

Added in new table to injection.md in addition to the old one (just so we can explicitly compare)

[ghost]

As far as I remember aakashs argument on the Max accelerating gradient was that some experimentally measured gradients were higher than the theoretical cold plasma wave breaking (that the classical formulas assume) limit- that's why we adapt our formula with this extra power. I think we should ask for a reference on this.

My concern-that I also already mentioned in class and he rejected - was that this might be only true for only very short distances, and not cm ranges.

[LeeEdel]

Oh, yes that sounds familiar. Thanks, Marlene.

I agree about asking for a reference.

[LeeEdel]

There are some other approximations for the gradient that I came across:

• uspas.fnal.gov/materials/11ODU/Laser-Plasma2.pdf (on slide "operational plasma density for laser-driven plasma accelerators")
• www.seas.ucla.edu/plasma/journals_files/files/journals/2007_Lu_prstab.pdf on page 6, 9

e.g. see appx.pdf

However, when I tried using these, I got nonsensical answers (just way off), so I likely was making a mistake somewhere. Someone else should try them and cross-check.

[Ossssip]

Not sure if I do it correct, but I have just plugged in the numbers into these formulas and the first formula gives the gradient of 0.25 GV/cm, and the second one gives the energy gain of 8 GeV over, I believe, our depletion length (16.9 cm), which gives about 0.47 GV/cm

[LeeEdel]

Ok, good. Thanks! I looked again today and got about the same numbers, so we're on the right track I think. The 0.47 GV/cm is also consistent with the equation from the book.

I asked over email about the output beam parameters and how to estimate them. It looks like these were from experimental results with similar laser parameters and gas densities (but I am waiting on confirmation of this), and they were written on the board in class. I would think having a different gas setup (e.g. multiple gas jets, no capillary, etc.) would likely throw those off, but without doing PIC simulations for this regime it is probably as close as we'll get.