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January 21, 2005



Thanks for the explanation Caolionn. I have always had trouble understanding th e role of plasma in advanced accelerators. Now I see blood has nothing to do with it.

Kit z brado

I am trying to understand the plasma wake but I have little insight about plasma so I have a few basic questions. I tried reading articles about it but I didn't have the patience for the theoretical approach - this is why I will try my luck here. Let's start with the phenomenology of the problem. I don't unerstand how the energy is pumped from the plasma - this is the point, right? My naive thinking leads to the conclusion that an electron bunch would be stopped in the plasma due to the electromagnetic interactions - instead of the opposite in your experiment. This is even more so if the figure above represents the real state in plasma: a wake behind the bunch where the electrons are depleted - this means that the electron bunch would feel attractive force from the wake (positive ions) and repulsive force from the electrons in the front. This would lead to velocity reduction. This is probably somehow connected with the "kick in the ass", that the bunch gets from the plasma electrons - I just can't see why this effect is so much greater than the attractive interaction. My last question/comment is about the energy gain figure that you wrote (impressive). What is the maximum energy achieved and what effect limits you?



Wow, lots of good questions. Let me see if I can take a first stab at them (some, hopefully, will be better explained in the blog over time).

.) Energy issues: It is a transformer in the sense that the energy from the head particles are transferred to the tail particles. Okay, so that means the head particles lose energy, but since they are relativistic, they don't stop the particles behind them that gain energy.

.) Ions and Electrons: The ions do not move on the time scale that the beam passes through the plasma, so they are not part of the wake. The wake is only composed of electrons from the ionized plasma. Having the ions stationary means they exert a nice focusing force on the electron bunch (also very good). The electrons in the wake all land behind the electron bunch, so there is a huge density spike on axis behind the bunch (sorry, that blue shaded region is supposed to be A LOT of plasma electrons, not ions, which I now realize it looks like). The density spike then administers the "kick in the ass".

.) Maximum energy gain: Really good question. The maximum wave (energy gain) we can get is called the wave-breaking field. In other words, the wave gets so large is collapses. The wave-breaking field is given by the following formula:

E_peak [V/m] = 96*sqrt(n_p[cm^-3])
where n_p is the density of the plasma. For a plasma with density 10^17 cm^-3, the maximum acceleration gradient is 30~GeV/m.

Kit z brado

A very fast response. Thanks.
.) Energy issues: If I understand your answers correctly than this means that your electron bunch that enters the plasma must be highly relativistic (what energies do you use?) and that it just transfers some of its vast amount of energy to the electrons in the plasma. So basically what you get is more electrons traveling along with the bunch - a plasma wave with its group velocity equal to the bunch velocity (right?).

.)Energy gain: what is the connection between the wave breaking field and the maximum energy-field is connected to the local electron density but I fail to see the connection to maximum electron energy.

One more: What happens when the wave collapses? You have electrons with huge energy - they cannot just vanish. Maybe you mean that a portion of those electron somehow outruns the bunch-they break of (hence wavebreaking field?)?


Hi Kit,

.) Energy issues: You got it. The incoming bunch is 28.5 GeV and the plasma wakefield mechanism adds about 3-4 GeV and causes energy loss on the order of 3-4 GeV. The energy perturbations are small compared to the incoming nominal energy.

.) Energy gain: OK, good point. The wavebreaking field tells you the maximum energy gradient, not the maximum energy gained by the particle(s). The maximum energy gained is dependent on the length of the plasma. This is an unknown, since we don't know how long of a plasma we can make using field ionization ( http://qd.typepad.com/13/2005/02/the_unbearable_.html ) before the beam becomes a big fuzzball and therefore worthless. Presently, we are limited by the facility where we work, otherwise we would like to answer that question.

.) Wavebreaking field: Ohhh, that is a tough question. Now that I have thought about it ... the wavebreaking field isn't surpassed. It is the physical limitation of the system. So the wavebreaking field merely tells you the maximum gradient your plasma density will provide. The wave never actually collapses - it is almost like there is safety mechanism which prevents you from exceeding its limitations. You can effectively run at the limit of the system without doing any damage. Thanks for asking that question, I hadn't thought about it in those terms.

Kit z brado

Hey Caolionn,

.)Energy issues: so this basically means that you don't really have any "gain". This is what bothered me in the first place. What you're really looking at is probably the increase in the number of electrons (generation of plasma) and the intensity of the electric fields created in the plasma wave.
Is there any application you have in mind using this phenomenon?

.) Wavebreaking field: this can be even more interesting for you than it was for me: you should check Nature Vol 431 (Sep 2004) pages 535-544. These are 3 articles about using intense lasers (P>TW) to generate plasma waves and furthermore to reach the wavebreaking limit where monoenergetic electron bunches are created (70 MeV). It seems to me that this is the regime where electrons are accelerated even further than in your experiment.


Hi Kit,

.) Energy Issues: We've only just begun!! Because of unforeseeable circumstances, we are presently limited to one bunch, where there is no net gain. What we are hoping for next is a two bunch experiment, where the first bunch ionizes and drives the wake and the second bunch "witnesses" the wake and gets accelerated. Then we trash the first bunch and use the second bunch. There is still the issue of sacrificing one bunch for doubling the energy of the other one, but it is still a cool option for upgrading already existing facilities.

.) Wakebreaking field: I saw the articles in nature, a collaborator wrote the intro article. The problem with laser-driven accelerators is being able to propagate the laser pulse for long distances. Many of those experiments run over distances of millimeters to a centimeter. However, laser-driven plasma accelerators have a nice potential to making the table-top type accelerator that everyone dreams about.

Kit z brado

Hi Caolionn,

This means that your goal is to achieve wake fields just below the wake breaking field which will accelerate the second bunch. This would mean that the distance between bunches would have to be about one plasma wavelength to achieve best acceleration (we're probably talking about energy gain of a few GeV). The only problem I see in this kind of an experiment (besides from the technical diffilcuties of course) are the EM forces between the bunches prior to entering the plasma - they may change the shapes of the bunches even though the repulsion in within individual bunches will be much greater.

Do you think that it would be possible to construct the pollowing experiment: you start with 2^n bunches - let's say 4. This means that you can accelerate 2 of these. This also means that you can also accelerate the final one (with less gain because of greater distance between the final two bunches). The exponent n could theoretically be as large as your plasma wave is - of course you could have problems with wave breaking in this case.


I'll be!

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