Title：XFEL and HHG interaction with matter: X-ray emission and effects of ultra-short pulses including random spikes
Speaker：Frank B. Rosmej 教授（巴黎索邦大学）
Time：May 4, 2021 (Tuesday) 21:00
Sponsor：Matter and Radiation at Extreme (MRE)
Bio：
Frank B.Rosmej教授/博士毕业于德国波鸿大学(Ruhr-Universität Bochum)，先后任职于波鸿大学、马克斯－普朗克研究所、德国重离子研究所(GSI)等。现任巴黎索邦大学教授(国家杰出教授)，强激光应用研究中心(LULI)“Atomic Physics in Dense Plasmas”研究团队负责人。长期从事教学科研工作，研究领域包括XFEL，聚变科学，高能量、高亮度光学激光，重离子束流与物质作用等。在Nature, PRL等期刊上发表过多篇论文。出版有专著Plasma Atomic Physics (2020年)。
And his he habilitated in 1998 he was then a professor in UN in Germany then in 2003 moved to the University of marsel and after that to the University of Sone in Paris where he is now a National Distinguished Professor um prizes included in 199 1 he
Was awarded the Fielder Lam prize in 2001 he was awarded the eminent scientist prize by riken in Japan and in 2013 he was awarded the kucho prize in Moscow um in 2019 he became an Adjunct professor from the Moscow Institute of Science of physics and technology and he
Was also awarded a lifetime award in atomic physics in 2019 he is an expert um for the European commission and the editor of pedagogical uh research papers in the international Journal J CNP his research interests are focused on x-ray free electron lasers radius of properties of matter Atomic physics x-ray spectroscopy applications of
Fusion science and Laser matter interactions and this year he has jointly published the book plasma Atomic physics with Springer so with that I’d like to welcome Frank and I will stop sharing my screen and Frank can start um can share his screen at the end will be the opportunity to ask
Questions okay so if you could just full screen is it okay now that’s perfect so if You’ just like to go ahead okay so today I would like to present some recent results concerning the interaction of xray and soft X radiation uh with meta and particular some applications uh to the free electron
Xray laser so after introduction some basic uh interaction processes for the XFL we will go in some detail for the XFL interaction with meta discuss some new role of atomic processes and then discuss some effects of ultra short pulses that have been published recently in the M
Journal so let us start uh with what happens in the case of op laser radiation interacting with mattera to make the contrast to the XFL so you have the inverse brm that means you accelerate the electrons the electrons are numers and the collisions between the electrons finally uh creates
What we call the electron Heating and the temperature uh in the system for the XFL the situation is very much different due to the high Photon energy the interaction with the free electrons is almost negligible and the main interaction is with the bound electrons of the mattera and of the
Atoms so the photon uniz ation creates a photo electron due to the high intensity there’s a large number of photo electrons they Collide and they create what we call the heating of the system how it interacts on a spatial scale so the optical laser up blades the surface creates a hot gas a
Plasma and in this plasma you can excite a lot of waves and the electron plasma wave can quickly come into resonance with the laser radiation and that happens usually at a density of 10 to 21 for the optical laser radiation so that means that essentially the laser energy is absorbed
At this so-called critical density and the laser beam cannot propagate uh from into the meta for the X-ray free electron laser the situation is completely different even for solid density for example for solid aluminum the solid plasma electron density is about 33 electron volt so that means that with an extra free
Electron laser in the range of kilo electron volt you will be able to penetrate deep into the so that means you have not absorption at the surface but you have absorption at the volume and therefore you have volumetric photoionization of inner Atomic shells and the role of atomic physics in
X-ray absorption for the optical laser is also quite different there is a z dependence so the absorption coefficient is proportional to Z so there is a big difference for example if you make the simulations for the heating of an aluminum Target or magnesium Target of course there are differences but they are relatively
Weak on the other hand for the xra free electron laser the dependence is very strong because as you fize in our shells if you are slightly above or slightly below some edges the absorption coefficients might drastically change in a very small energy interval by one two orders of magnitude so that means the
Absorption in XFL interaction experiment is strongly dependent on the atomic physics and the details of the atomic structure of the atoms and the ions so now let us discuss the XFL interaction with mattera that are related to short pulses and there are two effects in principle for short pulses one effect is
The meta Evolution itself due to the short pulse and the second is if you consider the elementary Atomic process there is a big difference between short PSE Theory and long PSE Theory which is somehow the traditional theory for the interaction so let us make some contrast for example to synchrotrons yeah for
Synchrotrons you also have x-rays you can interact with solids and you require why is that so much different with XFL which has the same energy of photons so first the XFL is an x-ray pulse in a very short time interval usually in the range of 10 some T of f to
Second the installations now provide almost standard focusing of the XFL beam and intensities of the order of 10 to 16 17 sometimes 10 to 18 are now rather stand at the installations and they even affords to go to even higher intensities up to 10 to 20 with submicron focusing
So if you calculate the photon density in the material you find that the number of photons per volume corresponds to almost solid density in the light pencil and that means that the XFL has approximately a Brilliance of 10 certain orders of magnitude higher than synchrons and you cannot simply say that
There are the physics is the same you just have more photons and everything will be more a better signal to noise ratio Etc but you see that if you change so many orders of magnitudes the physics is completely different and concerning the interaction of the target the difference is that for
Synchrotrons if you make a photoionization then the atomic perturbation by the synchrotron photon is a rare occasion in the solid but for the XFL due to this many orders of magnitude almost every atom is concerned so that means you change completely the material properties and that is the
Reason why the XFL has not just more Brilliance it allows to make completely different studies which are impossible with synchrotrons and this is small cartoon to understand what are the qualitative features so you have eometric photoionization that is an example for aluminum so you move out one electron
From the Cal by the photon of the XFL and create an photo electron and because you do this photoionization for almost every atom you have a lot of photo electrons so that means the photo electrons are quite numberous at near solid density so that means they can can considerably contribute to the heating
While in synchroton there is almost no Heating and by adjusting for example Photon energy you can tune this heating from D to some certain temperature then another important point and that is a main topic of uh the presentation today is about the time scale if you move out an electron from
Inner shell we know that there exists an effect in Tomic physics which is called o effect so that means if you have a hole in the atom the system is not stable but relaxes tries to refill this hole and the energy which somehow is released is sufficient to move out one electron and
This electron is called o electron now the important point is if you have as you have photons at near solid density you have more than one Photon per atom so that means you do this you create this whole states for every atom so that means on the time scale of f to
Second the macroscopic piece will not move so you have a sort of transient exotic piece of meta and that is called some sort of holoc Crystal which has hollow in the sense that there are only one or no electrons anymore in the inner shells and this example it was
The K shell so let us now uh discuss what is new in this this kind of processes because somehow all the atomic process o effect fot onization you know that since very very long but in relation to the XFL there is some sort of new role for this Atomic processes and that is
Illustrated here with a photo absorption so let us consider this light pencil in red and four photons and here is a solid Target indicated by three aluminum atoms so the photons go along and the first photon is interacting with for example the L shell the closed L shell
Is 2p6 configuration and the first Photon photo ionizes the configuration and what is left is 2p5 and one photo electron so now the light pencil is moving farther into the meta so what happens the second Photon comes in action but the first atom has already lost this electron so there is no
Appropriate energy level to interact with this Photon so that means the photon must go to the second atom ionize the 2p6 shell leave 2p5 create another photo electron and the same for the third Photon and you see you have created and that way three photo electrons now what happens with a fourth
Photon you see all atoms are already ionized there is no appropriate energy level to absorb this Photon so that means the absorption was so intensive and massive that there is nothing left for absorption and that means for this Force Photon the material became transparent but now we should
Consider that if that happens for every atom the number of photo electrons is near solid solid electron density and if electrons are near solid electron density and they are close nearby Atomic systems they induce three body Rec combination so that means the created State P5 is recombined by Rec
Combination and again the 2p6 is created and now the same atom can absorb one more that means can absorb the four electron Photon and create an photo electron so that means the laser can deposit two times energy to the same atom and that means there is no effective saturated absorption for the force
Electron and that means if you create the 2p6 state by this three body Rec combination and you absorb the force electron you are able to put more energy to the system because you can absorb also the force Photon so that means that the three body Rec combination it is not
Just an atomic physics process but it influences directly on the metah heating and this is a sort of new role in the XFL interaction with mattera so that is some simulation to see how many times uh an atom can absorb the photons and you see here on the left side number of absorbed
Photons per atom and that was done for an exfl 92 electron volt 50 F to Second here you see the intensity in logarithmic units and you see for intensities going to about 10 to 16 one atom absorbs many many times the photon so that means the phoned at is
Reproduced so that means for atoms Recreation is a real process and that is some simulation to demonstrate that the three combination effectively contributes to the heating because uh here artificially you have multipied the three body recombination by a factor of 0.1 so reduce this effect by a factor of 10 and
You see you considerably reduce the temperature this is a XFL pulse in blue this in black is a calculation where all processes are in like they are and in red where the three body Rec combination is very much reduced and you see that considerably influences on the temperature and
So it makes a sense to call that three body recombination assisted Heating and there is one more thing because you start from the solid and you create in a plasma you need Atomic physics from the solid until the plasma and let us consider the principle things for the O
Effect so that is a configuration where you have created a hole in the L shell and there’s three electrons in the valence band because the solid is still there because the interaction time of the laser PSE is very short so the solid is still there and what happens in OJ
Effect you refill it you move one electron out so that means in the valence band there is somehow one electron left plus another electron which is OJ electron so now let us look what happens in this re body Rec combination look the core which is for aluminum K2 L7 and the band
Structure is indicated the three electrons in the in the band structure the valence band structure are separated by two and by one electron and you see what happens when you go to the to this case of Rec combination you recombine one electron in the L shell you fill it
Up you have one electron left like in this three body Rec combination and if you compare these two configurations here and here you see that are they look formally very similar so that indicates that that in fact the process of OJ effect and three bodybody Rec combinations are somehow mutal to each
Other and you can write it in a general way the whole state two electrons in Valance band One in Valance band and on the right side the valance band electrons so the generalized body recombination generalizes the OJ effect and the body recombination that means if it is a solid it becomes the pure
Well-known OJ effect and if it becomes the plasma it becomes the three body Rec combination and if we had now explored that this re body Rec combination exists and leads to a heating that means that by this manner there must exist OJ heating too and this is uh the question
Uh that contributes considerably in the X-ray range because in the X-ray range the OJ electrons have very high energy which is almost of the same order like the ionization energy that means in the kilo electron Vol range and if you do a hole for every atom you have not only
Photo electron for every atom but you have an O electron after three body combination for every at so you can assume that you have a considerably heating induced by OJ effect and how to prove whether all that works in this way is to make some sort of independent
Diagnostics and that is via spectroscopy and that is soft x-ray spectroscopy but the problem here is if you use usual resonance line transitions they have transition probability which time scales of the order of 100 PC and you can diagnose almost nothing with this resonance line you can see
Them they are nice but they are not informative because they not really able to bring information about the signatures of the XFL interaction with the mattera so it is not possible to use standard spectroscopy but you you must base the spectroscopy on the whole states and that means that when you
Create or when you see the holes you should arrange your Diagnostic in this way that you see also the radiative channel of this Transitions and in that case your time scale is very short because the time scale is brought down by the OJ rate and that is of the
Order of 10 F Toc so you have radiation xray radiation on the time scale of the interaction and by this way we obtained an electron temperature of about 25 electron volt here and this coincided rather well with the simulations which is shown here for the range of interest of the intensity yeah there’s
Always some uh uncertainty in the intensity because of the focus spot size but within the arrow bar uh that looks quite reasonable so let us make a cartoon as a summary what happens with the short pulse interaction so you interact with the solid you interact with the inner shells
You create the photo electrons due to the whole creation you have OJ effect you have at the same time three body combination already from the photo electrons that contributes to the heating so the laser can be farther absorbed here three body Rec combination and OJ heating continue here and then
The heating destroys the crystal structure and you create something what is called warm dense matter and then if it goes farther a strongly coupled plasma so if you want to have a mechanical analog what happens you can look at the following picture yeah let’s assume you want to destroy this exhaust
So you put some explosion here marked and you see after the explosion it looks like the time scale is going this direction nothing happens and then you heat you heat farther and you see only after a considerable time after the explosion has started which corresponds to our
Case that the electron is removed from the system it leads to the mechanical destruction because you see the potential energy which is supported by the structure can now be released because the structure is destroyed and the same is in atomic physics if you remove the electron from the inner shell
You have a huge potential energy in the system and the system want to relax and therefore finally the system is destroyed so let us now come to the second effect of the ultra short pulses that is related to the atomic physics of the elementary process so uh in general
The interaction of photons with dense meta is described by the radiation transport equation so that means a light pencil propagates in X direction is locally absorbed by some absorption coefficient and intensity is increased because locally there can be also some emission here the formulas how to calculate the emission and
Absorption uh in blue is a point to calculate the emission and absorption coefficients you need two principle different theories one is atomic structure namely to calculate energies and transition probabilities and the second is you need atomic kinetics to calculate the atomic populations and you see that the absorption is related to the famous
Einstein coefficients and related uh to the spontaneous emission now let us pay attention to the part where the absorption happens so if you make an analysis of the dimension on the left and on the right side you will find that the product of the Einstein coefficient with intensity is in units
Of one over time so that means there is a number of transitions in a certain time per atom and to what does that correspond in a quantum mechanical approach so let us just consider a two-level system you have a photo absorption from level one and you populate level
Two so that means you have the wave function as you have only two levels the wave function is composed from the two stationary wave functions one and two but with time dependent coefficients because the radiation field perturbs the system in a Time dependent Manner and the probability to find the
System in the upper state two is given by the square of the amplitude for for level two and the number of transitions is therefore given by the time derivative of the squared of this amplitude now how to relate that to the transport equation or to Einstein theory
So this is very simple on the left you have the number of transitions which is a product of B and intensity on on right you have the quantum mechanical expression and it is well known that the Einstein coefficients they do not depend on time they are constants and you multiply that
With the intensity to calculate emission and absorption but you see in quantum theory all this is time dependent so the question is what about the time in this expression and we can answer this by perturbation Theory where you can calculate the amplitude in first order perturbation Theory and you find the following
Expression that is a matrix element of State one and two determined by the radiation field perturbation by the corresponding hamiltonian and the S squared function which is written here after some manipulations of this equation you obtain the famous so-called FIS Golden Rule rule where the transition is determined
By The Matrix element of the perturbation calculated with unperturbed States multiplied by time and this data function is just the energy conservation and you see because this expression is proportional to time the time derivative of T is one so that means this expression is independent of time and that
Means that corresponds this Independence corresponds to the Einstein coefficients that are crosssections and uh what quantum theory gives more one can ask yeah that allows just to calculate them because the Einstein theory gives only relations between them but you cannot explicitly calculate them because you have only two equations for three variables
So let us go to the meaning of this derivative as it is not dependent anymore on time that means that is a constant probability per unit time and this makes physically only a sense if you consider the process like averaged over many many cycles of the electromagnetic radiation because if you
Don’t have that you have face effects and all that should depend in time and cannot be this simple expression and that is harmful for Ultra short pulses because uh today you can go down even I I think the record is about 40 at seconds in the moment and that means few
Cycles or even sub Cycles but that means if you cannot use this expression then you cannot use crosssections and you must recalculate every case specifically with a multi-electron shreding ation and the interaction and that would be an absolutely terrible thing for any plasma physics for any interaction calculations
So this would be almost impossible to realize so the point is that the Einstein coefficients are in fact crosssections that the relation is given here for the absorption and if you lose the notion of the cross-section uh you really in a very misery situation so the question is uh is it
Possible to save standard cross-section for transition induced by Ultra short pulses and that can be done with a concept of probability for the total pulse which looks very attractive and that is due to a genius idea of valer asapa at M who derived an expression for the total pulse duration the
Probability which allows nevertheless to use the standard cross-section so that means on the left hand side there is not a probability per unit time anymore but there’s a total probability over the total pulse duration that is a standard cross-section and that is a fouryear transform of the ultra short pulse so it
May include any effect you like it might include the Face Effects it might be less than one cyle so it depends on what you put here for the foe transform so now let’s apply this Theory and that was our recent work uh we published in the
M uh to the xray free electron laser so in fact uh PSE durations of 10 100 F to Second they are very small small compared to z g rate and that induces considerable short piles effects in the evolution of the meta and in the exray emission but on the level of quantum
Theory this is still long because one cycle in the X-ray range has a Time duration which is a few other seconds only so and the question is uh what is the interest of the short PSE theory in the XFL because in the XFL the XFL has not a continuous pulse
But the XFL is in fact composed for many many spikes because it is a spontaneous amplification of spontaneous emission so these are pulse spikes and if you look at the measurements you see that each Spike has a VD of only 0.1 0.2 ftoc while the envelope which characterizes the pulse
Duration is of the order of a few or few T ftoc so that means short pulses are inside this random spikes in the XFL pulses so we made a study uh by a model function so the electric field is written down in this way so
That means it is a blue curve that is regular spikes if you take the phases every every time the same and this time characterizes the time of the envelope and this tow characterizes the width of the spike and now let us look what happens to the photoionization for example of
The K shell of aluminum which is about at 1.6 KV Omega C is a so-called carrier frequency in this diagram n is the number of spikes it’s 24 here in the simulations t is the envelope duration which is 15 F to Second and to spike duration so the diagram is in terms of
The spike duration and of the phiz probability normalized to the energy in the pulse because of course if you reduce uh the duration you reduce the energy so that would give you a trivia dependence in the diagram which is removed by this normalization and you see that for ra
Long pulses of the spikes it is constant so that means that corresponds to F’s Golden Rule or to other uh perturbation Theory well known results that there is a transition probability per unit time and here you see that if the pation becomes very short you see there is even a
Highly nonlinear dependence in this probability and this are the calculations for for many different different energies so you see that the short pulse effect due to the short pulses in the spikes is of considerable importance so let us apply that to the slope analysis of the K absorption edge of aluminum so
Take a single gausian pulse of which 20 F to Second and take a temperature of two electron volt temperature of six electron volt so you know due to the family distribution the slope changes and this can be used for example for the determination of the electon temperature
So this are the black and the blue solid curves and now let’s make a simulation you have 50 spikes in the 20 fto seconds and one spike is 0.1 ftoc that is a red one and you see that is for the room temperature and you see that the short pass effect
Creates likewise a slope so that means spiky pulses in XF radiation induces slopes near the edge okay then that is the explication uh in general the spikes are randomly distributed so we make made a random uh simulation of the parameters that means we took random phases etc etc and then we
Calculated the photoionization probability for the Ked and the results are presented here and you see uh the random calculations are the solid lines in different colors and the different colors yeah here red blue and so on they correspond to different simulations set up with random parameters so you start your simulations with different
Parameters so that give different random curves and of course if it’s completely random that should be rather similar and you see that that is seen here and what is also indicated here in the dash line that are the spikes which are assumed to be regular why that is interesting because
For the real application if you have random spikes and you want to calculate them uh you can do that artificially but how to do that for an experiment usually you don’t have available all the parameters for the random spikes so that would be a great harm for
For some recalculations so we try to investigate what are the real dependencies of this random parameters so in general they are not well known and that would be a great harm but you see that the calculation for the regular spikes are not very much different they are slightly different as you see for
Example here compared to the random p as you see for example here but the General tendency and the general digs are very close so it seems that random parameters do not enter strongly in the probability for the photo processes compared to regular spikes and for this purpose uh we have developed another
Analytical model which is called the mathematical expectation model and yigo has do a very important work here to derive all this equations so they are given in this uh publication so you can use this mathematical expectation model the formulas are very big so I cannot put them really on the transparency but
They can be used in order to simulate in an analytical way and with a small sub protein uh this effect so let us conclude uh the XFL interaction with meta creates exotic meta called holoc Crystal because you can remove one 2K ho electrons the corhole photoionization drives massive o and photo electrons
That results into a heating also the three body Rec combination Heating and you can identify uh this scenario with independent x-ray spectr scopy by determining the temperature and comparing with the simulation and due to the influence for the heating yeah there’s a new role of the atomic physics processes and because you
Go from the solid to the plasma you can somehow speak about generalized Atomic processes the next impact is on a pure Atomic physics level for elementary process the concept of probability per unit time is very questionable for Ultra short laser pulses and the presented Ultra short P Theory
Allows nevertheless the use of standard cross-sections and this is probably the only way it is not yet realized but uh this is ongoing research uh this is probably the only way how to calculate really the interaction of systems and use standard cross-sections and calculate the heating and other
Processes the XFL spikes are of very short duration and those the spikes are subject to the ultra short P Theory and what we have demonstrated is that if you make random parameter variation there is a little difference compared to regular spikes and that allows to derive an analytical model for
The spike effects in this rather long nevertheless short on ftoc level but on spiky level rather short to derive some general expression for a usual spiky XFL PSE thank you for your attention great well thank you so much um Professor rajm fascinating talk so um
I see we have so the the way that we normally run questions is that the guests raise their hands um and then I will unmute them and they can ask their question in person so I see we have two uh two questions here we’ll start with David kandle who I will allow to
Talk so if you just un mute yourself thank thank you Frank it was a great talk for an old Atomic physicist who can sort of remember some Atomic physics uh is there any role for a dielectronic recombination or is it just too small compared to three body recombination back in the hollow
Case uh the dielectronic recombination plays not an important role of course it’s included the atomic physics process and it can be generalized with the inverse process because in fact first you have D electronic capture and if it results uh in the capture of an electron after relaxation it’s called dielectronic
Recombination and that usually gives you the possibility to see the emission from alizing States and that is what I had presented here so uh in fact if you do that uh analysis you see that some part what you see here this is D electronic satellite emission from this States yeah
And you create the Hole by the photon and then you hit the plasma and due to the heated plasma you act again on the L8 state by dielectronic capture so you have additional intensity from the dielectronic recombination which you use for the evaluation so uh
This is a tricky way uh in order to make uh the diagnostic but the influence itself on the heating is not so large thank you okay thanks very much so um next we have Vladimir um thank you Frank this very nice and very pedagogic presentation my question
Goes to this last part about the Broadband uh uh laser X XFL laser spectrum and con ution with the cross-section yeah could we interpret it like your laser is really very bra Broadband it it covers several spectral lines and your transitions are very narrow so just you’re just taking a certain
Spectrum uh wids from your laser to excite such and such transition this is include in this integral yes because this is as this is a f transform so it’s number photons yeah so that means you have a spectrum indeed of photons and that’s why here there is the integral to take into
Account this this effect so that means in this expression the effect of the spectrum is included but it is not not the only one because uh if you make the fya transform of an abitrary pulse it can have also an arbitrary face and if you look at the expression of quantum
Mechanics you see in order to go to familyy Golden Rule you need to remove this part this is a so-called Broadband illumination to remove that from the integral yeah in order to make from the integral this proportional T that means that you assume that this integral is equivalent
To the Delta function limit so your monochromatic laser um yeah yeah somehow yes so this function deforms uh to a monochromatic part but you see in the turbation Theory uh there is not only this part of monochromatic and non- monochromatic there is a question of this complicated time
Dependence so there are two things related to this approximations with the integral with the time dependence and the effect that the spectrum is brought and you see if you have this expression here what you do effectively to derive this expression you start from the very beginning of the perturbation
Theory and make the fo transform directly in perturbation Theory and consider the duration for the whole perturbation and then you derive your amplitudes and then you come to this equation so it is not just just that you move in a Broadband emission so there are many
Effects I think what you losing here the phases so no no no no the phase can be included here I just didn’t write it yeah but you taking absolute value so you taking number of photons but you do not consider correlation coherence between different spikes uh you can you
You can you can you can you uh if you take a a short PSE for example like I showed you uh the F transform can contain the face and if you have a pulse duration less than one cycle you have the phas in the probability and if you
Calculate it you see that there’s a face effect in the probability okay thank you okay thank you very much Vladimir so next up we have de Hoffman if you’d like to need and ask a question hi Frank um great talk ah hi this is DJ calling from Shanghai I’m on
My way back to Germany P I have a question assume you have a DT or proton Boron solid and do this would this eventually change the rate of uh fusion um I don’t think so because usually the time evolution of the compressed capsule is in the range of
Let’s say at least T of PICC and ten of PICC uh is too long for the optical laser for example if you have one uh electron volt you have one cycle has a duration if I remember right uh I think it is four yeah maybe in in some tense of a second yeah
So that means the duration of the pulses are still to long to to see something like like this okay thank you okay do we yes we have one more question so Kayan would you like to unmute and ask question and yes so Frank very good talk
Can you hear me yes I can hear you okay yeah so just now you talk about o Heating and H straight body and recommendation heating so what’s the difference between the two kind of heating Mechanics I just want to know that so uh so the question is about the relation between the O and the combination yes about the heating heating about the heating so I think we can um go to this figure so um at the first instant of interaction you remove by the XFL
Photons an electron and that is the photo electron so the photo El have near solid density and that means in that moment they already make this three body Rec combination and you can absorb some more photons so that means uh the photo electrons have of course some kinetic energy that is the
Energy which is left and that is the energy difference between XF and the and the edge energy and because you have created the hole you have the the OJ effect but because it is inner shell it is also in the range of the energy of
The XFL itself so that means that are K electrons and again because you have a hole everywhere you have an OJ electron everywhere so that means you have a lot of solid density OJ electrons at KV energy so that means that that you heat
Up that is an energy in K range and if that collides you establish a temperature and then this body Rec combination happens again and you see the OJ electrons the photo electrons and the three body Rec combination they all three contribute in the curse of time to the heating and
Then all is over is recombined and then then you go farther with the with a meta Evolution and it depends how you tune your laser for example if you tune Junior laser that you just move out the electron there’s almost no energy in the photo electrons but you recombine them
Yeah so that that depends strongly on the relation of energy and uh and atomic configurations okay but Frank I think I have a different explanation from you uh at least for three recommendation I think for the straight body Rec combination I I think it’s due to the
Cor section the um electrons with are at lower velocity you know for how say for the max valan distribution I mean the Velocity in the velocity space and so some some electrons has higher velocity and some electrons has lower velocity so for those electrons which has lower um
Um velocity they have a larger crosssection Force straight body recommendation so that means the the electrons at a lower velocity or at a lower energy they they combined so uh average speaking the electrons um I mean the free electrons they have higher energy they are left in the free Staters
So finally uh the recomm the the electron temperature the average the electron temperature looks higher so I I think at least for the how say straight body accomodation um normally we think in that way we think of their corse so I I think maybe for the Al Al um process
Maybe the same but I don’t know you you can try to say yeah uh of course it depends on the temperature in general the three body Rec combination has the asmt one over t squared over temperature so in depending on the temperature of course three body recombination is high
Or low but uh that’s why I have shown you this figure here so you see here yeah so that is a typical situation for an experiment so this is 10 to 16 wat per square cm this is 92 electron volt 50 F to Second and
You see uh you heat up to about 40 electron volts and then if you reduce three body recombination by a factor of 10 you go down to 20 electron volt so you see uh of course it depends all on the relations of atomic system as I told
And the energy but you see that in this realistic experiments which have been uh performed uh some time ago you see that this body Rec combination effectively contributes to the heating despite of the fact that 40 electron volt is rather high but the density is also rather High it is near solid
Density of the electrons okay so Frank I trust your result I just want to know the explanation okay thank you yeah okay thank you very much Kayan okay so um if there’s I actually have one question so you showed that the uh there’s this Broad of the kedge as a
Function of the spike duration I wondered if that’s which your models predict as wondering if that’s something that’s been could be investigated experimentally or has been investigated experimentally um this slope is used for the analysis of uh the temperature de determination particular the I know the group in in
Bordeaux with Fabian Doris and other so they made experiments and they used the slope of the spery distribution for the determination of the temperature yeah and that can be done in general without problems if the PSE is very long for example uh if you heat it with u with long pses Etc so
This pulse or this shape is used to determine rather low temperatures which is otherwise would be difficult so you need some sort of high resolution spectroscopy so that you resolve this Edge slope of course that is usually very noisy and then you can try to fit uh this this
Slope and this was just an example example to show that for realistic parameters for example you have a few electron volts for this pulse and if you take it spiky uh there could be induced slopes which could be seen say could could you deliberately change the say the spike duration and
Look for this alteration in the slope um to change the spike duration on purpose in an experiment that would be a very difficult thing yeah but I remember uh some Publications where the people discuss that uh to produce the exfl with a single Spike which is very of very short
Duration and there are some theoretical papers uh published even some years ago so uh maybe we will have available in some years at the XF the possibility to have a single Spike and you can change this duration MH that would be really interesting I think we should oh do we
Have one more question in the chat uh says great talk this is from lyen hang says great talk besides the orgo heating and three body assisted heating could you also comment on the competing excitation de exitation processes for the heating ah okay so uh this we have studied also it was
In fact shown but I didn’t speak about that um you see here uh that is the collisional unionization yeah so you see if you switch off any posess which avoids energy heating or increases it you influence for example if you see if you reduce the collision unionization by a factor of
10 then you see the electrons don’t lose this energy and you increase the temperature yeah and and that is in here in green and in red you see as already discussed if you reduce this re Body by a factor of 10 well uh you see that you reduce the
Temperature and you can do that for any process so that means of course if you reduce the exitation it would have a similar effect like unionization here yeah so that means that you would move this curve up but then at the same time you should consider the
Exitation yeah and you would have a similar effect like on the on the red curve yeah so that would be the effects and somehow this is artificial factors yeah and you cannot say to switch one process off because if you do that in the simulations that is a sort of kitchen
Yeah and if you change one thing you change the others also but this gives you some impression where are the the effects okay thank you very much I think we should probably call it a day here there are actually more questions in the Q&A tab but maybe if we um uh not sure
If there’s I don’t I think we should probably finish now so um perhaps you’ve got Frank’s uh email address which is shown here so um perhaps people could contact him directly if they have questions okay so just like to close by thanking uh Professor Ro BOS M once
Again and for a fascinating talk and uh we’ll see you next time okay thank you for the organization and invitation hope to see you next time okay bye bye