As in the beginning, that is, it is required to accelerate in highly focused fields, in which the longitudinal component of the electric field is significant, but in such fields the phase velocity of the wave along the propagation axis is greater than the speed of light, so the electrons quickly lag behind the accelerating field. To compensate for the latter effect, it was proposed to conduct acceleration in gas, where the relative permittivity is higher than unity, and the phase velocity decreases. However, in this case, a significant limitation is that even at radiation intensities of the order of 10 14 W / cm², the gas is ionized, forming a plasma, which leads to defocusing of the laser beam. Experimentally, this method was used to demonstrate the modulation of 3.7 MeV of a beam of electrons with an energy of 40 MeV.

Acceleration in a plasma wave

When a sufficiently intense laser pulse propagates in a gas, it is ionized with the formation of a nonequilibrium plasma, in which due to the ponderomotive action laser radiation possibly the excitation of the so-called wake wave - a Langmuir wave traveling after the impulse. This wave contains phases in which the longitudinal electric field is accelerating for electrons traveling with the wave. Since the phase velocity of the longitudinal wave is equal to the group velocity of the laser pulse in the plasma, which is only slightly less than the speed of light, relativistic electrons can be in the accelerating phase sufficiently long time acquiring significant energy. This method of accelerating electrons was first proposed in 1979.

As the intensity of the laser pulse increases, the amplitude of the excited plasma wave increases and, as a consequence, the acceleration rate increases. At high enough intensities, the plasma wave becomes nonlinear and eventually collapses. In this case, a highly nonlinear regime of propagation of a laser pulse in a plasma may arise - the so-called bubble (or bubble) regime, in which a bubble-like cavity is formed behind the laser pulse, almost completely devoid of electrons. This cavity also contains a longitudinal electric field that can effectively accelerate electrons.

Experimentally, an electron beam was obtained in the linear interaction mode, accelerated to energies of the order of 1 GeV on a path 3 cm long.To compensate for the diffraction divergence of the laser pulse, in this case, a waveguide in the form of a thin capillary was additionally used. An increase in the laser pulse power to the petawatt level made it possible to increase the electron energy to 2 GeV. A further increase in the energy of electrons was achieved due to the separation of the processes of their injection into the accelerating plasma wave and the acceleration process itself. In 2011, this method obtained electrons with an energy of about 0.5 GeV, and in 2013 the level of 3 GeV was exceeded, and the total length of the accelerating channel was only 1.4 cm (4 mm - injection stage, 1 cm - acceleration stage) ... In 2014, the first experimental results on the acceleration of electrons in a 9 cm long capillary using a BELLA laser. In these experiments, acceleration to an energy exceeding 4 GeV by a 0.3 PW laser pulse was demonstrated, which became a new record.

In the nonlinear regime of interaction, the maximum achieved energy was 1.45 GeV on a 1.3 cm long path. In the experiment, we used a laser pulse with a power of 110 TW.

see also

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Notes (edit)

1. R. Joel England et al. Rev. Mod. Phys. DOI: 10.1103 / RevModPhys.86.1337.
2. E. Esarey, P. Sprangle, J. Krall(English) // Phys. Rev. E. - 1995. - Vol. 52. - P. 5443.
3. T. Tajima, J. M. Dawson(English) // Phys. Rev. Lett. ... - 1979. - Vol. 43. - P. 267.
4. W. P. Leemans et al.(English) // Nature Physics. - 2006. - Vol. 2. - P. 696-699.
5. Xiaoming Wang et al.(English) // Nature Communications. - 2013. - Vol. 4 . - P. 1988.
6. B. B. Pollock et al.(English) // Phys. Rev. Lett. ... - 2011. - Vol. 107. - P. 045001.
7. Hyung Taek Kim et al.(English) // Phys. Rev. Lett. ... - 2013. - Vol. 111. - P. 165002. - DOI: 10.1103 / PhysRevLett.111.165002. - arXiv: 1307.4159.
8. W. P. Leemans et al.(English) // Phys. Rev. Lett. ... - 2014. - Vol. 113. - P. 245002. - DOI: 10.1103 / PhysRevLett.113.245002.
9. C. E. Clayton et al.(English) // Phys. Rev. Lett. ... - 2010. - Vol. 105. - P. 105003.

Literature

Scientific

• E. Esarey, C. B. Schroeder, W. P. Leemans(English) // Rev. Mod. Phys. ... - 2009. - Vol. 81. - P. 1229-1284.
• K. Krushelnick, V. Malka(eng.) // Laser & Photon Rev. ... - 2009. - Vol. 4 . - P. 42-52.
• A. V. Korzhimanov, A. A. Gonoskov, E. A. Khazanov, A. M. Sergeev// Phys. - 2011 .-- T. 181. - S. 9-32.
• V. Malka Laser plasma accelerators // Phys. Plasmas. - 2012. - Vol. nineteen . - P. 055501. - DOI: 10.1063 / 1.3695389.
• S. M. Hooker Developments in laser-driven plasma accelerators // Nature Photonics. - 2013. - Vol. 7. - P. 775-782. - DOI: 10.1038 / nphoton.2013.234.
• R. Joel England et al.(English) // Rev. Mod. Phys. ... - 2014. - Vol. 86. - P. 1337. - DOI: 10.1103 / RevModPhys. 86.1337.
• I. Yu. Kostyukov, A. M. Pukhov(rus.) // Phys. - 2015 .-- T. 185. - S. 89. - DOI: 10.3367 / UFNr.0185.201501g.0089.

Popular science

• L. M. Gorbunov// Nature . - 2007. - No. 4.
• V. Yu. Bychenkov// Science and life . - 2010. - No. 12.

Excerpt characterizing laser acceleration of electrons

Arriving in St. Petersburg, Pierre did not inform anyone of his arrival, did not go anywhere, and began spending whole days reading Thomas of Kempis, a book that was delivered to him by some unknown person. Pierre understood one thing and all while reading this book; he understood the pleasure he had not yet known to believe in the possibility of achieving perfection and in the possibility of fraternal and active love between people, opened to him by Osip Alekseevich. A week after his arrival, the young Polish Count Villarsky, whom Pierre knew superficially from the Petersburg world, entered his room in the evening with the official and solemn air with which Dolokhov's second entered him and, closing the door behind him and making sure that there was no one in the room except Pierre was not there, he turned to him:
“I have come to you with an errand and a proposal, Count,” he said to him without sitting down. - A person who was very highly placed in our brotherhood petitioned that you be accepted into the brotherhood ahead of time, and invited me to be your surety. I regard the fulfillment of the will of this person as a sacred duty. Would you like to join the fellowship of free stone-makers for my guarantee?
The cold and stern tone of the man whom Pierre saw almost always at balls with an amiable smile, in the company of the most brilliant women, struck Pierre.
“Yes, I wish,” said Pierre.
Villarski bowed his head. - One more question, Count, he said, to which I ask you not as a future Freemason, but as an honest man (galant homme) to answer me with all sincerity: have you renounced your previous convictions, do you believe in God?
Pierre pondered. “Yes… yes, I believe in God,” he said.
“In that case…” Villarsky began, but Pierre interrupted him. “Yes, I believe in God,” he said again.
“Then we can go,” Villarsky said. “My carriage is at your service.
Villarsky was silent all the way. When Pierre asked what he needed to do and how to answer, Villarsky only said that his brothers, who were more worthy of him, would test him, and that Pierre needed nothing more than to tell the truth.
Having entered the gates of a large house where the lodge was, and walking along a dark staircase, they entered a lighted, small hallway, where, without the help of a servant, they took off their fur coats. From the front they went into another room. A man in a strange outfit appeared at the door. Villarsky, coming out to meet him, said something quietly to him in French and went up to a small wardrobe, in which Pierre noticed clothes he had never seen before. Taking a handkerchief from the closet, Villarsky put it over Pierre's eyes and tied it in a knot at the back, painfully capturing his hair in a knot. Then he bent him to him, kissed him and, taking his hand, led him somewhere. Pierre was in pain from the hair pulled in a knot, he winced in pain and smiled in shame of something. His huge figure, with downcast hands, with a wrinkled and smiling face, followed Villarsky with irregular timid steps.
After taking him ten paces, Villarski stopped.
“Whatever happens to you,” he said, “you must endure everything with courage if you are firmly resolved to join our brotherhood. (Pierre answered in the affirmative by tilting his head.) When you hear a knock at the door, you will untie your eyes, added Villarsky; - I wish you courage and success. And after shaking hands with Pierre, Villarsky went out.
Left alone, Pierre continued to smile in the same way. Once or twice he shrugged his shoulders, brought his hand to the handkerchief, as if wishing to take it off, and again lowered it. The five minutes he spent with his eyes bound seemed to him an hour. His hands were swollen, his legs were giving way; it seemed to him that he was tired. He experienced the most complex and varied feelings. He was both terrified of what would happen to him, and even more terrified of not showing fear to him. He was curious to know what would happen to him, what would be revealed to him; but most of all he was glad that the moment had come when he would finally embark on that path of renewal and an actively virtuous life, which he had dreamed of since his meeting with Osip Alekseevich. Strong blows were heard at the door. Pierre took off the bandage and looked around him. The room was black - dark: only in one place was a lamp burning in something white. Pierre came closer and saw that the lamp stood on a black table, on which lay one open book. The book was the gospel; that white, in which the lamp was burning, was a human skull with its holes and teeth. Having read the first words of the Gospel: “In the beginning there was a word and a word was with God,” Pierre walked around the table and saw a large open box filled with something. It was a coffin with bones. He was not at all surprised by what he saw. Hoping to enter into a completely new life completely different from the previous one, he expected everything extraordinary, even more extraordinary than what he saw. The skull, the coffin, the Gospel - it seemed to him that he had expected all this, expected even more. Trying to evoke a feeling of tenderness in himself, he looked around him. “God, death, love, brotherhood of people,” he said to himself, associating with these words vague but joyful ideas of something. The door opened and someone entered.
In a weak light, to which Pierre had already managed to take a closer look, a short man entered. Apparently, having entered the darkness from the light, this man stopped; then, with careful steps, he moved to the table and laid on it small hands covered with leather gloves.
This short man was dressed in a white, leather apron that covered his chest and part of his legs, a sort of necklace was worn around his neck, and a tall, white frill protruded from behind the necklace, bordering his elongated face, illuminated from below.
- Why did you come here? - asked the newcomer, after a rustle made by Pierre, turning in his direction. - Why are you, who do not believe in the truths of the light and do not see the light, why did you come here, what do you want from us? Wisdom, virtue, enlightenment?
The minute the door opened and an unknown person entered, Pierre experienced a feeling of fear and awe, similar to that which he experienced in confession in childhood: he felt himself face to face with a completely stranger in terms of living conditions and with loved ones, in a brotherhood of people. human. Pierre, with a breathtaking heartbeat, moved up to the rhetorician (this was the name of a brother in Freemasonry who prepares a seeker to join the fraternity). Pierre, coming closer, recognized in the rhetoric a familiar person, Smolyaninov, but he was offended to think that the person who had entered was a familiar person: the person who had entered was only a brother and a virtuous mentor. For a long time Pierre could not utter a word, so the rhetorician had to repeat his question.
“Yes, I… I… want renewal,” Pierre said with difficulty.
- Well, - said Smolyaninov, and immediately continued: - Do you have any idea of ​​the means by which our holy order will help you in achieving your goal? ... - said the rhetorician calmly and quickly.
“I… hope… guidance… help… in updating,” Pierre said with a trembling voice and with difficulty in speaking, both from excitement and from the habit of speaking in Russian about abstract subjects.
- What concept do you have about Frank Freemasonry?
- I mean that Frank Freemasonry is fraterienit & eacute [brotherhood]; and the equality of people with virtuous goals, ”said Pierre, ashamed, as he spoke, of the inconsistency of his words with the solemnity of the moment. I mean…
“All right,” said the rhetorician hastily, apparently quite satisfied with this answer. - Have you looked for a means to achieve your goal in religion?
“No, I considered it unjust and did not follow it,” Pierre said so quietly that the rhetorician did not hear him and asked what he was saying. - I was an atheist, - Pierre answered.

Plan:

Introduction

• 1 Direct acceleration by laser field
• 2 Acceleration in a plasma wave
• 3 Notes
Literature
• 5.1 Scientific
• 5.1.2 Popular science

Introduction

Laser acceleration of electrons- the process of accelerating an electron beam using ultra-strong laser radiation. Both direct acceleration by electromagnetic radiation and indirect acceleration in a Langmuir wave excited by a laser pulse propagating in a low-density plasma are possible. This method experimentally obtained electron beams with energies exceeding 1 GeV.

1. Direct acceleration by a laser field

Direct acceleration by a laser field is ineffective, since in a strictly one-dimensional problem, an electron entering the field of a laser pulse, after leaving it, has the same energy as at the beginning, that is, acceleration is required in highly focused fields in which the longitudinal component of the electric field is significant. but in such fields the phase velocity of the wave along the propagation axis more speed light, so the electrons quickly lag behind the accelerating field. To compensate for the latter effect, it was proposed to conduct acceleration in gas, where the relative permittivity is higher than unity, and the phase velocity decreases. However, in this case, a significant limitation is that even at radiation intensities of the order of 10 14 W / cm², the gas is ionized, forming a plasma, which leads to defocusing of the laser beam. Experimentally, this method was used to demonstrate the modulation of 3.7 MeV of an electron beam with an energy of 40 MeV.

2. Acceleration in a plasma wave

When a sufficiently intense laser pulse propagates in a gas, it is ionized with the formation of a nonequilibrium plasma, in which, due to the ponderomotive action of laser radiation, it is possible to excite a so-called wake wave - a Langmuir wave traveling after the pulse. This wave contains phases in which the longitudinal electric field is accelerating for electrons traveling with the wave. Since the phase velocity of the longitudinal wave is equal to the group velocity of the laser pulse in the plasma, which is only slightly less than the speed of light, relativistic electrons can be in the accelerating phase for a sufficiently long time, acquiring significant energy. This method of accelerating electrons was first proposed in 1979.

As the intensity of the laser pulse increases, the amplitude of the excited plasma wave increases and, as a consequence, the acceleration rate increases. At high enough intensities, the plasma wave becomes nonlinear and eventually collapses. In this case, a highly nonlinear regime of propagation of a laser pulse in a plasma may arise - the so-called bubble (or bubble) regime, in which a bubble-like cavity is formed behind the laser pulse, almost completely devoid of electrons. This cavity also contains a longitudinal electric field that can effectively accelerate electrons.

Experimentally, an electron beam was obtained in the linear interaction mode, accelerated to energies of the order of 1 GeV on a path 3 cm long.To compensate for the diffraction divergence of the laser pulse, in this case, a waveguide in the form of a thin capillary was additionally used.

In the nonlinear regime of interaction, the maximum achieved energy was 1.45 GeV on a 1.3 cm long path. In the experiment, we used a laser pulse with a power of 110 TW.

3. Notes

1. E. Esarey, P. Sprangle, J. Krall Laser acceleration of electrons in vacuum - dx.doi.org/10.1103/PhysRevE.52.5443 (English) // Phys. Rev. E... - 1995 .-- T. 52 .-- S. 5443.
2. T. Tajima, J. M. Dawson Laser Electron Accelerator - dx.doi.org/10.1103/PhysRevLett.43.267 (English) // Phys. Rev. Lett.... - 1979 .-- T. 43 .-- S. 267.
3. W. P. Leemans et al. GeV electron beams from a centimetre-scale accelerator - www.nature.com/nphys/journal/v2/n10/full/nphys418.html // Nature physics... - 2006. - T. 2. - S. 696-699.
4. C. E. Clayton et al. Self-Guided Laser Wakefield Acceleration beyond 1 GeV Using Ionization-Induced Injection - dx.doi.org/10.1103/PhysRevLett.105.105003 (eng.) // Phys. Rev. Lett.... - 2010 .-- T. 105 .-- S. 105003.

Literature

5.1. Scientific

• G. Mourou, T. Tajima, S. V. Bulanov Relativistic optics - rmp.aps.org/abstract/RMP/v78/i2/p309_1 (English) // Rev Mod Phys... - 2006. - T. 78. - S. 309-371.
• V. S. Belyaev, V. P. Krainov, V. S. Lisitsa, A. P. Matafonov Generation of fast charged particles and superstrong magnetic fields in the interaction of ultrashort intense laser pulses with solid targets - dx.doi.org/10.3367/UFNr.0178.200808b.0823 // UFN... - 2009 .-- T. 178 .-- S. 823.
• E. Esarey, C. B. Schroeder, W. P. Leemans Physics of laser-driven plasma-based electron accelerators - rmp.aps.org/abstract/RMP/v81/i3/p1229_1 (eng.) // Rev Mod Phys... - 2009 .-- T. 81 .-- S. 1229-1284.
• K. Krushelnick, V. Malka Laser wakefield plasma accelerators - dx.doi.org/10.1002/lpor.200810062 (eng.) // Laser & Photon Rev... - 2009. - T. 4. - S. 42-52.
• A. V. Korzhimanov, A. A. Gonoskov, E. A. Khazanov, A. M. Sergeev Horizons of petawatt laser systems - ufn.ru/ru/articles/2011/1/c/ // UFN... - 2011 .-- T. 181. - S. 9-32.

5.1.2. Popular science

• L. M. Gorbunov Why do we need super high power laser pulses? - vivovoco.astronet.ru/VV/JOURNAL/NATURE/04_07/LASER.HTM // Nature. - 2007. - № 4.
• V. Yu. Bychenkov Fifty years of the laser. A new step - an accelerator on the table - www.nkj.ru/archive/articles/18951/ // Science and life. - 2010. - № 12.

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This abstract is based on an article from the Russian Wikipedia. Synchronization completed 07/19/11 11:25:29 AM
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Charged particle accelerators have long ceased to be exclusively scientific instruments. Today in the world there are more than 30 thousand accelerators, and most of them are used for radiation therapy of cancer, sterilization and the production of semiconductor materials. For example, to turn a pure silicon wafer into a microchip, you need to insert impurity atoms into strictly designated places, and an accelerator is perfect for this. The more compact, reliable, and cheaper the accelerators are, the more profitable they are to use and the more new tasks can be found for them.

In the first accelerators with the help of high voltage, a powerful electrostatic field was created, which picks up and accelerates charged particles. But a generator capable of delivering over a million volts is complex, expensive, and difficult to use. Such a voltage can create an electrical discharge towards other objects at a distance of more than a meter. Today, instead of a constant voltage, particles are accelerated by applying an alternating electric field to them many times.

Description

This is how all modern accelerators work, but this method has already reached its limit. To develop such devices further, many physicists are studying the possibility of accelerating charged particles by the field that occurs when laser radiation interacts with matter. Laser pulses can concentrate energy in very short bursts and thus provide extremely high power without building complex installations.

To accelerate particles (protons, for example) with a laser, physicists in recent decades have been directing laser pulses onto a thin foil. In this case, the electromagnetic field accelerates part of the electrons inside the light wave, as a result of which they fly through the foil, creating two oppositely charged areas in the material. And where there are two areas charged with the opposite sign, there is also an electric field, which can then pick up the particles and give them the necessary impulse.

Read also:

Previous experiments with laser beams and foil have shown that it is possible to knock out protons with energies up to 8 MeV from the material. This corresponds to the energy that an electron would receive if it flew between points with a potential difference of 8 million volts. This is already sufficient for many practical applications of accelerators, but not enough for medical accelerators. For example, for proton therapy of cancer, particles with energies over a hundred MeV are usually used.

And it is for the targeted burning of tumors that it is important to create as cheap accelerators as possible. The fact is that now for these purposes it is necessary to build complex synchrotrons weighing hundreds of tons, so there are only about fifty places in the world where proton therapy can be carried out (there are several of them in Russia). Naturally, the cheaper such a device is, the more they can be built and the more lives can be saved.

Description

New publication in Communications Physics describes a slightly modified approach: instead of one powerful pulse with an energy of 1.1 joule, Swedish physicists proposed to take two pulses of 0.55 joule each. In practice, this means that one pulse is divided into two using a semitransparent mirror. Two beams fall on the foil at a certain angle, and, as shown by modeling, this significantly increases the energy of the emitted protons at no additional cost. According to the calculations of scientists, the scheme with two beams increases the maximum energy of protons to 14 MeV.

But for medicine, this is still not enough. The protons obtained during the interaction of laser radiation also have a too wide spectrum, the energy of the particles is unevenly distributed between them, and some move noticeably slower than others. But the proportion of particles that received energies above 1 MeV increased fivefold. This allows us to count on further progress in this area. The researchers emphasize that the laser beam can be divided into more parts. It is possible that the correct selection of the beam configuration will make it possible to achieve even better results.

Hello, my name is Alexander and I am a physicist. From the outside, this may sound like a verdict, but in fact it is. Turns out that I'm doing basic research in physics, namely, I study accelerated charged particles: protons and all those that are larger - positive ions, that is. In research, I do not use large accelerators like the LHC, but shoot a laser at the foil, and a proton pulse is emitted from the foil.

Now a few words about me. I graduated from the Faculty of Photonics and Optoinformatics of ITMO in St. Petersburg, then went to the magistracy at Aalto University (this is in Finland) in the direction of micro- and nanotechnology, and then spat on all these little things, microscopes, and especially on a clean room. And I went into basic science with large lasers. Now I am working in graduate school in the southwest of Sweden in the city of Lund at the university of the same name. It's about a cannon-shot distance from Copenhagen.

As accelerated, and flew

Charged particle accelerators themselves are not a new idea, but the method by which I accelerate them is relatively fresh, about my age. It can significantly reduce the size of the accelerator and its cost, including the cost of operation and maintenance. The difference between the two types can be seen in the picture below.


On the left is an electrostatic linear accelerator (slightly disassembled); On the right is my little but proud foil hole maker

Let's take a closer look at these two examples of grim physical genius. Look at the left accelerator and the right one, then again at the left one and again at the right one: yes, mine is on horseback (joke - author's note). In fact, mine is only a meter in diameter, and the protons themselves are accelerated from a piece of foil. Its holder is located exactly in the middle of the circle, it is wearing a beautiful copper skirt. It is much simpler and more compact than the left sample, which is the size of a bus and is also filled with asphyxiant gas. So, having self-asserted enough (in physics it often happens that the less the better), you can turn to the physics of the acceleration process.

Since we accelerate charged particles, it is most logical to do this with an electric field. We will characterize the field as tension. For those who went to the front and back end after school, let me remind you: electric field strength - vector physical quantity, which characterizes the electric field at a given point and is numerically equal to the ratio of the force acting on a stationary point charge placed in this point field, to the value of this charge(dirty copy-paste from Wikipedia). Has the dimension V / m. Coming back to comparison, the accelerator on the left accelerates protons to 4 MeV (Megaelectronvolt), that is, 2.77 * 107 m / s or 9.2% of the speed of light. Since the charge of the proton is 1, and the length of the accelerator is two meters, the field strength will be 2 MV / m. Here we have assumed that in all places the field is directed in the same direction and, in general, were very close to the truth. A stylish accelerator has a field strength of the order of several TV / m, that is, about a million times more. Still, we have to admit that its length is only a few microns.

So, at this point we have figured out whose field is steeper. Now is the time to turn to the physical and engineering mechanisms that this field creates. In the case of a conventional accelerator, there are two metal sheets, one of which is negatively charged, and the other in no way. Remember the school experiment about rubbing an ebony stick with a piece of wool. Here the principle is absolutely the same, but the execution is much more complicated. If protons are accelerated from the foil, then the field is created by electrons, electrons fly out of the hot plasma, the plasma is produced and heated by the laser, and the rest of the post is about all this.

Do you want me to knock it and it turns purple speckled?

If you hit hard enough, you can see many wonderful physical phenomena... This is how the guys at Harvard got metallic hydrogen and then lost it.

In my case, I shoot at the foil with a laser. I will describe it in more detail after explaining the non-trivial physics of the processes of obtaining warm dense matter, this is how plasma is scientifically called, which is the culprit for the triumph of the acceleration of my protons. And now about everything in order.

The laser generates pulses with a wavelength of 800 nm and 35 fs with a duration (10 -15 s), that is, the real pulse length in a vacuum is about 10 µm. This impulse contains about 2 J of energy, which is a lot. If we take this pulse and focus it on the foil into a neat round spot 5 µm in diameter, then the intensity will be about 10 20 W / cm 2. This is already an obscene amount. Again, a little comparison: steel can be safely cut at an intensity of 10 8 W / cm 2 (or so).

In fact, the laser pulse, due to the design of the amplifier, has a previous pedestal with a duration of about 500 ps, ​​and this very pedestal greatly helps to accelerate protons well.

Ionized means armed

Let us recall what happens to light when it enters a substance. Energy must be conserved, which means there are only three options for events: reflection, transmission and absorption. In a harsh life, all of the above are present at once. In fact early stage we are interested in takeover.

So, we have a pedestal, which we also focus perfectly on a piece of foil, and it is absorbed there perfectly. In order not to go into the complexity of physics solid, consider the absorption of a detached atom. From quantum mechanics we know that only a photon can be absorbed, the energy of which is exactly equal to the energy of the transition of an electron from one state to another. If the photon energy is greater than the ionization energy (that is, sending an electron from the parent's nest on a free trip), then the excess will go into the kinetic energy of the electron, everything is simple. In our case, photons with a wavelength of 800 nm do not have enough energy (this is the energy of one photon, not the whole pulse!) To ionize the target, but here physics comes to our aid. Remember I mentioned the high intensity of the radiation? If, in addition, we remember that light can be represented as a flux of photons, and the intensity is directly proportional to it, then it turns out that the flux of photons is very large. And if the flux is so large, then there is a high probability that several photons will arrive at the same place and at the same time, and when their energy is absorbed, they will add up, and ionization will still happen. This phenomenon, oddly enough, is called multiphoton ionization, and we regularly use it.

At the moment, we have that the electrons have been successfully torn off, which means that the main pulse arrives at the ready-made plasma and begins to heat it.

Plasma physics fundamentals (no joke, ah)

Before heating it is worth telling a little about plasma as a state of matter. Plasma, it is like a gas, only electrons are separate, and nuclei are separate. We will consider our plasma as an almost ideal gas, but consisting of electrons.

Of our main characteristic plasma will be its density (the number of electrons per unit volume), we will further denote this value by $ n_e $ (not to be confused with the refractive index!), and the temperature of these very electrons, that is, their average speed of movement. This is described by the Boltzmann distribution in the same way as in the school physics course:

$$ display $$ \ frac (m_e v ^ 2) (2) = \ frac (1) (2) k_B T_e, $$ display $$

from which it follows easily

$$ display $$ \ langle v \ rangle = \ sqrt (k_B T_e / m_e), $$ display $$

where $ inline $ k_B $ inline $ is the Boltzmann constant, $ inline $ T_e $ inline $ is the electron temperature, and $ inline $ m_e $ inline $ is the electron mass. Yes, here we considered a one-dimensional case, but we really don't need more to describe our processes.

We now apply an electric field to the plasma already described. Let me remind you that plasma consists of charged particles, which means that at a given density, at a certain distance from the place where we applied the field, electrons will obscure (screen) the source (such a crowd of little Matrosovs - author's note). The distance that is needed for this is called the Debye length and is given by the equation

$$ display $$ \ lambda_D = \ sqrt (\ frac (\ epsilon_0 k_B T_e) (q ^ 2_e n_e)). $$ display $$

Here $ inline $ q_e $ inline $ is obviously the electron charge, and $ inline $ \ epsilon_0 $ inline $ is the dielectric constant of the vacuum, such a fundamental constant. Let's analyze this formula a little to see the simple physics of the process behind it. By increasing the density of electrons, we decrease the average distance between them, as a result, in a shorter distance we collect enough electrons to completely screen our field. On the other hand, the higher the temperature, the greater the average distance between electrons.

Due to the screening effect and the quite definite (from temperature) average velocity of the electrons, the plasma does not react instantly to the suddenly arriving field. It is logical to assume that the response time is related to the Debye length and the electron velocity. A good analogy is throwing a stone into a lake. Compared to the whole lake, the stone acts on the surface of the water pointwise. Part of the water changes immediately (this is where it flopped), and then the waves begin to spread over the water surface. In the case of plasma, the sudden electrical field is a stone. The size of the flop is determined by the screening length (the field does not act beyond it), and the propagation of waves depends on how close the electrons are to each other. We can introduce a characteristic such as the response time of the plasma:

$ inline $ t_D = \ lambda_D / v $ inline $. By and large, it shows us the time it takes for information about the change in the applied field to reach those electrons that did not seem to see this field.

Since we are physicists, we do not like time very much. It is much more convenient to work with frequencies, so we will introduce the concept of the natural frequency of a plasma. This value will show us how often we can change the field so that the entire accumulation of electrons, which we proudly call plasma, has time to react to these changes. Well, what could be easier? We divide 1 by the response time, and here it is - the frequency:

$$ display $$ \ omega_p = \ frac (1) (t_D) = \ sqrt (\ frac (q ^ 2_e n_e) (\ epsilon_0 m_e)). $$ display $$

It is easy to see that the natural frequency of plasma oscillations depends on the electron density. The more electrons, the higher the frequency. Another analogy can be drawn, but this time with a spring pendulum. The high density of electrons tells us that they are closer to each other, and therefore interact more strongly. Let us assume that their interaction is directly related to the elasticity of the pendulum spring. And the more elastic, the higher the vibration frequency.

The natural frequency of a plasma also determines its refractive index. If you honestly write the wave equation of the collective motion of electrons in a plasma, and then assume small changes in the electron density (we will not do this here, because this is boring), then the refractive index is set as follows:

$$ display $$ \ eta = \ sqrt (1- \ frac (\ omega ^ 2_p) (\ omega ^ 2_0)). $$ display $$

Here $ inline $ \ omega_0 $ inline $ is the circular frequency of the applied electric field. It is in rad / s and not in Hz!

Let's take a closer look at this expression. As an experimental physicist, I do not like real numbers, and I try to ignore complex numbers, especially the complex refractive index. Well, how can light, after all, spread in matter in i times slower than in a vacuum? This is some kind of nonsense! Actually not, but more on that another time. If $ inline $ \ omega_0> \ omega_p $ inline $, then the expression has a real value, and the alternating electric field propagates inside our plasma. Everyone is happy, and we will call such a plasma not dense enough. However, if $ inline $ \ omega_0< \omega_p$inline$ , то показатель преломления становится не то что комплексным, а целиком мнимым. В этом случае (и не просто потому что я так захотел) волна вообще не будет там распространяться, а сразу отразится без потерь. Это слишком плотная плазма. Очень классное явление, кстати. Называется плазменным зеркалом.

And as dessert $ inline $ \ omega_0 = \ omega_p $ inline $. This is a plasma of critical density. In this case, it begins to enter into resonance with the forcing (supplied by us) alternating electric field. For such special occasion you can even introduce the concept of critical density and set it like this:

$$ display $$ n_c = \ frac (\ epsilon_0 m_e \ omega ^ 2_0) (q ^ 2_e). $$ display $$

Naturally, for each frequency of the driving field, the critical density is different.

SHOCK! Plasma heating! For this you only need ...

In our case, we will focus on only one heating mechanism, which prevails in the experiment.

To begin with, let the plasma that we formed on the pedestal have a smooth density gradient, in this case we have heating through resonant absorption. An illustration of this in the picture below.

Illustration of the resonant absorption process: a) the distribution of the electron density near the front side of the target; b) refraction of a laser beam in a plasma with a density gradient; c) electric field in plasma

So, the laser shines on our plasma at an angle, well, let it be 45 degrees, and at the same time it is polarized in the plane of incidence. Polarization is indicated by red arrows in the figure. Our plasma has a density gradient, which means that its refractive index is constantly changing (here it is growing). At some point, it will happen that a certain layer of plasma for our laser will become "turning" and it will be reflected, that is, for some time it will propagate parallel to the critical layer. It is important to note that it will rotate before it reaches the critical density layer, since we launched it at an angle to the normal. The plasma density at which the laser beam rotates is given by the following equation:

$$ display $$ n_t = n_c \ cos ^ 2 \ alpha, $$ display $$

where $ inline $ n_c $ inline $ is the critical density and $ inline $ \ alpha $ inline $ is the angle of incidence of the light.

Now the fun begins. Let us recall that light is not only a stream of photons, but also an electromagnetic wave, that is, our impulse has an electric field that oscillates harmonically with a large amplitude. When light propagates parallel to the critical layer, a standing wave is formed, which does not change over time (naturally, as long as the laser pulse is in place). The field of this wave, in fact, penetrates beyond the layer of plasma where the light turned, and reaches the critical layer. Let me remind you that the frequency of plasma oscillations in the critical layer is the same as the frequency of laser radiation, which means that resonance occurs. When the laser stops shining, the energy that it has imparted to the electrons in the critical layer is distributed through impacts to the rest of the electrons, which means that the plasma has heated up.

So where, in fact, is the acceleration?

Now that we have warmed up the electrons in the plasma well, and the laser no longer shines, we can tell how protons are accelerated. To do this, take a look at the pictures below. Until this moment, I never said where the protons come from at all. Naturally, they do not come from the cores of the foil material. Since we are not very neat and do not wear gloves (hands sweat heavily in them), water and hydrocarbons appear on the surface of the foil. Ionized hydrogen is our invaluable source of protons. Checked: if you remove the pollution, then there will be no protons.

	Plasma formation by a pedestal, that is, ionization of the front side of the target. Foil with a thickness of 0.4 - 12 μm is usually used as a target.
	Here, the bulk of the pulse interacts with the created plasma and heats it up. Some electrons are so well warmed up that they fly out with back side target.
	When enough electrons have escaped, the remaining positive charge in the foil pulls them back. In plasma, they heat up again and fly out. For a while, a dynamic equilibrium is established. The electric field is directed perpendicular to the target
	This very electric field strips off protons and other ions (depending on what was there at all) from the back surface of the target, and then accelerates them. By the time the ions have accelerated, the electron cloud is already falling apart, and all the particles begin to fly further together. And then we begin to believe that they do not interact anymore.

Divide and rule

At the moment, the position is as follows: the laser has not shone for a long time, there is a hole in the foil, protons with electrons fly together from the target normally to its rear surface. We do not need electrons at all, so a magnet comes to the rescue here. When a beam of charged particles flies through a magnetic field, the Lorentz forces deflect each particle in proportion to its speed and charge. Accordingly, protons and electrons will deviate in different directions, and we will simply not look in the direction of electrons. By the way, the more the energy of the proton (that is, its speed), the less it will deflect. This means that by placing a small screen that is sensitive to protons, we will be able to see the energies of accelerated protons. A few more comparisons in numbers: the magnet that we have is permanent and creates a field of about 0.75 T; in MRI machines the magnetic field is 1.5 - 3 T.

In addition, we can see the profile of the proton beam in flight. It's round, by the way. And if we can also measure the energy of the protons in each part of the beam, we will be able to unambiguously reconstruct the shape of the electron cloud, which accelerated our protons.

Instead of a conclusion

A fair question may arise as to why all this is needed. My favorite answer is just like that. This is a fundamental science, and it is pointless to try to find momentary applications for it. Perhaps in some years it will find its application in the treatment of cancer or thermonuclear fusion, but for now the main task is to learn something new about the world around us, just like that, because it is interesting.

For those who are especially curious about the laser itself and its device

As promised, here I will tell you about the laser, with which I do science. I have already mentioned some of the characteristics of our laser, but I did not talk about the pulse repetition rate. It is approximately 80 MHz. This frequency is determined only by the length of the resonator and is the reciprocal of the time it takes for the light to travel back and forth through the resonator. Looking ahead, I will say that it is impractical to amplify the pulses at such a frequency, it is incredibly difficult from an engineering point of view, and you cannot save enough electricity.

I will not go into laser theory especially. The basics of where laser radiation comes from is excellently laid out in the Wikipedia article on stimulated radiation. If we try to be very brief, then three components are needed for laser radiation: an active medium (photons are emitted from it), pumping (it maintains an active medium in a state in which there are more excited atoms that can emit), and a resonator ( it ensures that photons copy each other on multiple passages through the active medium). If you put all the ingredients together and pray, then the laser will begin to shine, but continuously. If you try more, you can make it generate impulses, including such short ones as on my installation. For the most curious, the method of generating femtosecond pulses is called passive mode locking. And now a small feature of very short pulses. It is often believed that a laser shines at the same wavelength, and in continuous mode, as well as at long pulses, this can even be called true. In fact, due to a number of complex physical processes, which we will certainly not discuss here, the temporal shape of the pulse and its spectrum are related by the Fourier transform. That is, the shorter the pulse, the wider its spectrum.

Let's say that we started the master oscillator, but the energy of its pulses is a few nJ. Remember in the beginning I said that the energy in a pulse that arrives at the target is about 2 J? Now, this is a billion times more. This means that the impulse must be strengthened, and we will talk about this in more detail.

Short pulses are generally characterized by very high peak powers (remember, divide energy by time?), And this has a number of complications. If on Wednesday shine radiation with a high intensity (power per unit area), then it will burn out, and if the active medium has burned out, then nothing will be amplified. That is why we choose a repetition rate of 10 Hz and only amplify them. Since there is a lot of equipment and all of it operates at exactly this frequency, we have a special box that distributes these 10 Hz to all hardware, and for each device you can select the delay in receiving a signal with an accuracy of several picoseconds.

There are two ways to deal with high intensity. As you might guess from its definition, you need to either increase the area or reduce the power. With the first, everything is very clear, but the second method was a breakthrough in laser technology in the twentieth century. If the impulse is initially very short, it can be stretched, amplified, and then compressed again.

To understand how to do this, let's turn to the basics of optics. For different wavelengths, the refractive indices in the medium are different, which means (by the definition of the refractive index, by the way) that with an increase in the refractive index, the speed of propagation of light in the medium decreases. And so we launched our pulse on Wednesday, and its red part passed the material faster than the blue one, that is, the pulse became longer, and its peak power dropped. Hurray, now nothing is burning! For a deeper knowledge in this area, I recommend to google and read about the amplification of chirped pulses (aka Chirped Pulse Amplification or CPA).

All we have to do is amplify the momentum, squeeze, focus and send it to make a hole in the foil!

And now some pictures with captions.

The actual photo of the laboratory. The cylindrical crap in the middle is a vacuum chamber, because protons fly very lousy in the air and bump into its molecules all the time. Well, in general, everything looks cooler with a vacuum. The blue thing on the right is a lead wall, so as not to accidentally get superpowers and radiation sickness. The laser itself is located behind the door, which is on the left with a yellow Achtung sign

And here is the wall itself in profile. Yes, inside it is filled with lead, like Winnie the Pooh.

Our command post is located behind the wall, when we shoot, it is necessary to sit behind it for safety reasons. Of course, we will not die from radiation, but you can easily go blind. There are five monitors for two computers, it's very easy to get lost in all this junk. One of the computers has speakers, so while working in the dungeon you can listen to Loboda and the Big Russian Boss, for some inexplicable reason my colleagues also like them. Only half of them are Swedes, by the way.

We also have a lead compartment door. It is hydraulically driven.

Here we are inside the laser room. This is a photograph of the first table on which a laser pulse is generated. Here it is pre-amplified (approximately 1000 times) and stretched. On the top shelf there is a bunch of very important and necessary electronics, without which the laser will not work.

This is the second table in which the radiation is amplified after the first. This amplifier is our main workhorse - it boosts energy forty thousand times. In fact, it contains two amplifiers of different design: multipass and regenerative. In the first, the impulse simply passes through the active medium several times. The second has its own resonator. With the help of electro-optical shutters (Pockels cells), the pulse is launched inward, it passes there several times until the gain is saturated, and then it is released further. This is where the speed and accuracy of opening and closing the gates are so important.

This is the third table, here the amplification is about 15 times. The tower in the middle, which protrudes above the lid, is a cryostat. In it, in a vacuum, there is a hefty crystal that is cooled by liquid helium to a temperature of -190 degrees Celsius.

This is a separate room that houses the pumping power supplies of the third table and the main vacuum pumps. The efficiency from the outlet of the system is so-so, about 0.1%. I once calculated that the electrical power consumption was about 160 kW. It is about 960 video cards that can be powered and mined, mined, mined. This is how much electricity is consumed when amplified at a repetition rate of 10 Hz. If we tried to amplify 80 MHz, then the consumption would increase 8 million times.

Thank you for your attention!

Secondary beams

In modern experiments, secondary particle beams are widely used, which are created after the interaction of the primary accelerated particle beam with the target. Using electromagnetic separators and collimators, from the huge number of particles formed on the target, it is possible to separate particles of a certain type and a certain momentum. In nuclear physics, in this way, secondary beams of radioactive nuclei are obtained, the lifetime of which can be several milliseconds. Similarly, you can get secondary beams of p- and K-mesons. Secondary beams of p-mesons can be used to form neutrino beams, which are obtained by decay of p-mesons:

p-> m- + n m, p +> m + + nm.

A clean neutrino beam can be obtained by filtering the resulting particles through a thick absorber.

Laser acceleration of electrons

The idea of ​​using lasers to accelerate electrons in plasma was put forward in 1979 by American scientists. With regard to short laser pulses, the first analytical research were published in 1987 and 1988. In fact, laser acceleration of electrons in a plasma is very close to the so-called collective method of electron acceleration, which was developed for many years at the Kharkov Institute of Physics and Technology under the leadership of Ya.B. Feinberg. One can read about the problems faced by the traditional vacuum accelerator technique and about collective methods of acceleration in plasma in the article published earlier in the journal “Priroda”.

Rice. 57

Dotted lines show lines of lowered electron density, solid lines - lines of increased electron density. The arrow shows the direction of propagation of the laser pulse.

As applied to short laser pulses, the acceleration of electrons in a plasma can be schematically represented as follows. Propagating in the plasma, the pulse pushes electrons out of the region where it is currently located (Fig. 3). In addition to the forces from the impulse, the electrons are acted upon by the electric field from the plasma ions, which can be considered stationary due to their greater mass... After the pulse has left this region, only the charge separation field acts on the electrons, striving to return the electrons to their original position. Having accelerated in this field, the electrons slip past their initial position and begin to oscillate relative to the ions at the so-called plasma frequency. Since the pulse runs through the plasma and all the time pushes out those electrons that meet in its path, it starts plasma oscillations behind it all the time. In this case, the initial phase of these oscillations is different at different points along the path of the pulse. As a result, a charge separation wave is excited, the phase of which propagates through the plasma with the pulse velocity (the so-called wake wave, Fig. 4). The electric field of this wave in one half of the period is directed in the direction of pulse propagation, and in the other half of the period - opposite to the direction of pulse propagation. If an electron with an initial velocity equal to the pulse velocity is placed in that region of the plasma wave where the force acting on it from the side of the electric field is directed in the direction of its motion, then the electron, moving along with the wave, will begin to accelerate. Such an accelerator is called a “wake-wave accelerator”. For relativistic particles, the speed of which is close to the speed of light, even a small increase in speed corresponds to a large increase in their energy. As a result of acceleration, the energy of the electron can increase significantly.

Rice. 58 - Perturbation of the electron density in a wake wave excited by a laser pulse with a duration of 30 fs and a power of ~ 30 TW in a plasma with a density of 2.2 · 1018 cm-3. The vertical axis is the radial coordinate measured from the pulse axis. On the horizontal axis - the time after the passage of the laser pulse through this point

Experiments carried out in France have shown that the mechanism of electron acceleration described above is actually realized. But the resulting increase in the electron energy turned out to be insignificant due to the very small length at which this acceleration occurred.

At first, it was believed that laser pulses with a duration close to the period of plasma oscillations are best suited for exciting wake waves, while longer pulses are not suitable for this purpose. But numerical calculations and subsequent experiments have shown that this is not the case. A laser pulse, the length of which significantly exceeds the length of the plasma wave, and the power exceeds a certain value, changes its shape during propagation in the plasma (Fig. 5). First, modulation of its amplitude occurs, and then it is divided into a sequence of shorter pulses with a repetition period equal to the plasma period. This effect is called self-pulse modulation. A resonance arises between the sequence of short pulses and the plasma oscillations. Each subsequent short impulse increases the amplitude of the wake wave that was excited by the first short impulse. As a result, already inside the laser pulse, the plasma wave field becomes very large and reaches 109 V / cm. Part of the plasma electrons is then captured in the plasma wave. They begin to move with the wave and accelerate to an energy of about 100 MeV over a length of several millimeters.

Rice. 59

On the initial pulse with an intensity smoothly varying in space (left figure), first amplitude modulation (middle figure) appears, and then it is split into a chain of short-length pulses (right figure), the distance between which is equal to the plasma wavelength lp.

Experiments carried out in France, USA, Japan, England have shown that in the self-modulation mode the maximum energy of accelerated electrons is quite high, but energy spectrum turns out to be very wide, which is a disadvantage from the point of view of possible applications.

In 2004, almost simultaneously, three experimental groups discovered a new regime of electron acceleration, in which the energy reached 250 MeV, and the energy spectrum was rather narrow. In this regime, the laser radiation intensity exceeded 1019 W / cm2, and the pulse length was close to the plasma wavelength. The high-frequency pressure forces acting on the plasma electrons were so great that an almost spherical region appeared immediately behind the pulse, in which there were practically no electrons. This area was called bubble, and the acceleration mode itself was called the bubble mode (Fig. 6). A number of plasma electrons were captured from the plasma into this region, which were accelerated.

At present, considerable experimental and theoretical material sufficient for the design and construction of a laser accelerator with an electron energy of more than 1000 MeV. Several such projects are now close to implementation.

Rice. 60 - Propagation of a laser pulse in the bubble-mode. Immediately behind the pulse, a region is formed in which there are no electrons (an electron bubble). A small electron bunch is captured into it from the plasma, which is accelerated

proton particle detector acceleration

In 2000, when thin foils were irradiated with high-intensity (more than 1018 W / cm2) laser pulses, protons with energies up to 10 MeV were detected, escaping mainly from the rear wall of the foil in the direction of pulse propagation. This result aroused great interest. The experiments were repeated in many laboratories. The maximum measured energy of protons in some of them reached 60 MeV, and their number reached 1012 per laser pulse.

How do protons with such high energies come about? Analysis of the experimental data and numerical calculations showed that under the action of a laser pulse, fast electrons appear in the foil, which pass through the foil and fly out from its opposite side. But they cannot fly far. They are stopped by the electric field of the ions remaining in the foil. A negatively charged layer consisting of electrons is formed near the rear surface of the target. The electric field created by these electrons is directed perpendicular to the surface and reaches a value sufficient to ionize the atoms on the surface. Then, under the influence of the same electric field, the ions begin to accelerate. A double layer is formed, consisting of layers of electrons and ions separated in space, which is emitted from the target. In the process of acceleration, energy is transferred from electrons to ions. Light ions (protons) formed from hydrogen atoms adsorbed on the foil surface are most effectively accelerated (Fig. 61).

Rice. 61 - Acceleration of ions (protons) when irradiated with a short laser pulse of a thin foil. The laser pulse falls on the left boundary of the foil, fast electrons fly out through the right boundary of the foil and accelerate the ions with their electric field

Such sources of energetic ions are already finding application in proton radiography, when an image of an object is obtained by shining through it with a proton beam. This method manages, in particular, to determine the structure of electric fields inside the investigated object. But laser sources of fast ions have the greatest prospects in medicine (oncology). The fact is that it is protons that are more expedient to use to influence cancerous tumors. At present, the sources of such protons are various vacuum accelerators, which are very bulky and expensive. It is hoped that laser sources will turn out to be more compact and cheaper.