In Laser Plasma Acceleration (LPA) , an ultra short laser pulse generates a plasma wave with relativistic phase velocity via the ponderomotive force. Particles can be accelerated, with electric fields up to three orders of magnitude larger (>100 GeV/m)  than conventional radio frequency accelerators, in a range covering from tens of MeV to GeVs [3, 4] with fs duration , excellent emittance at the plasma-vacuum interface (∼1 mm.mrad), high peak current (1-10 kA) and percent energy spread  within cm scale. Nevertheless, the best LPA parameters are not achieved simultaneously. Different configurations (laser wakefield accelerator (LWFA) , plasma beat wave accelerator (PBWA) , self-modulated LWFA , wakefields driven by multiple pulses  and the highly nonlinear regime of electron cavitation ) offer distinct characteristics. In the generation of the electron bunch by LPA, two phases can be differentiated, injection, during which the electrons are injected into the wave forming the beam, and boost where the electrons of the beam gain energy. The method used for injecting the electrons in the bubble (colliding pulse regime [9, 10], density ramp injection , ionization injection [12, 13, 14]) determines the characteristics of the LPA system.
source identification in the electron heat transport model. This phenomenon is described by a second-order parabolic differential equation with distributed diffusion parameter and input. Once existence and uniqueness conditions of the heat model solution are established, a spectral Galerkin method is used to express this solution in the finite dimensional frame- work. The time-space separation and the Kalman filter are combined to simultaneously estimate the distributed variables (diffusion coefficient and the input). Computer simulations on both simulated and real data are provided to illustrate the performance of the proposed technique.
We have thus shown the remarkable capability of the κ-ε model to cap- ture key aspects of the physics of turbulent transport throughout the plasma. The present simulations, which are first tests of the model, use a single scalar as tuning parameter to describe the whole 2D dependence of the turbulent diffusion coefficient. The confrontation to experimental data is quite con- vincing, both for midplane and divertor profiles. The width of the energy exhaust channel is also recovered in L-mode simulations of TCV and WEST. Further adjustment of the model can be achieved using experiments and/or micro-turbulence simulations. It is to be noted also that the model can be used to model the core plasma as well as self consistent transitions to im- proved confinement regimes. As also analyzed in the paper, the non-linear dependence of the diffusion coefficients could allow one extending the use of such transport modeling to transients. This modeling effort would no longer be restricted to steady state as the usual diffusive ansatz would imply. Sim- ilarly, because the diffusive coefficients governing the transport of the two fields κ and ε are defined to depend non-linearly on their values, typically like κ 2 /ε, the transport dynamics can depart significantly from that stem- ming from fixed diffusion processes. Finally, in the present implementation of the model a single instability drives the turbulent fluctuations on the ion characteristic length scale. The model can be completed using other instabil- ity growth rates and one could also split the model according to fluctuations on either ion or electron scales.
• Particle (PIC-MCC) simulations are very powerful but due to constraints on the grid spacing and time step, cannot be used for the high plasma densities and large volume of the negative ion source. We have discussed in this paper how simulations performed under conditions of smaller plasma densities (‘scaling’), although not ‘exact’, can provide a very useful insight in the physics of the source, and that the results can often be linearly extrapolated to the real densities with a good approximation. Care must however be taken when the sheaths play an active role in the discharge or in the simulation of negative ion extraction (and when instabilities and turbulence are present ). One important conclusion of the ‘scaled’ PIC-MCC simulations is the demonstration that the presence of the magnetic ﬁlter can induce a strong asymmetry in the plasma properties in the direction parallel to the PG. This is because the diamagnetic and E ´ B drift in the magnetic ﬁlter region are not closed, as in closed-drift sources (Penning source, magnetron discharge, Hall thruster etc...) but are directed toward a wall. This induces a Hall effect which generates the plasma asymmetry and enhances electrontransport though the ﬁlter. Calculations performed with a large scaling factor tend to show that the plasma asymmetry leads to a signi ﬁcant non-uniformity of the negative ion current density along the extraction apertures. The validity of linear extrapolation of this result to the real conditions of plasma density is difﬁcult to prove but nevertheless, these simulations raise the question of beam uniformity.
force is a force directed away from the outer divertor target. When detailing the contribution of the different forces it appears that the friction with D + (solid red line) flushes O down towards both divertor targets, whereas the deuteron thermal gradient force (blue solid line) pulls O away from the lower divertor. The two corresponding electron forces (dashed lines) have similar trends but are characterised by values smaller by one order of magnitude. The overall net force acting on O ions (black solid line) is in favour of the thermal gradient forces at both divertor targets but it is ' 3 times stronger at the outer one, resulting in the depletion of the O concentration in this region as observed in figure 8.a and 10.b.
It is well known from experiments that magnetized low-temperature plasmas in devices such as Hall thrusters and ion sources often show the emergence of instabilities that can cause anomalous transport phenomena and strongly affect the device operation. In this thesis we investigate the possibilities to simulate these instabilities self-consistently by fluid modeling. This is of great potential interest for en- gineering. We used a quasineutral fluid code developed at the LAPLACE laboratory, called MAGNIS (MAGnetized Ion Source), solving a set of fluid equations for electrons and ions in a 2D domain per- pendicular to the magnetic field lines. It was found that in many cases of practical interest, MAGNIS simulations show plasma instabilities and fluctuations. A first goal of this thesis is to understand the origin of the instabilities observed in MAGNIS and make sure that they are a physical result and not numerical artifacts. For this purpose, we carried out a detailed linear stability analysis based on disper- sion relations, from which analytical growth rates and frequencies were successfully compared with those measured in MAGNIS simulations for simple configurations forced to remain in a linear regime. We then identified these linear unstable modes and their responsible mechanisms (involving parameters such as the density gradient, electric and magnetic fields and inertia), known from the literature, that are likely to occur in these fluid simulations. Subsequently, we simulated the nonlinear evolution and saturation of the instabilities and quantified the anomalous transport generated in different cases relevant to ion sources, depending on various key parameters of the system (electric and magnetic fields and electron temperature). Finally, we highlighted several limitations of MAGNIS, and more generally of fluid models, due to the physical approximations made (quasineutrality, absence of kinetic effects). We showed that the fluid modes are sometimes most unstable at infinitely small scales for which the theory is no longer valid and which cannot be resolved numerically. We proposed, and tested in MAGNIS, ways to overcome this problem by introducing effective diffusion terms representing small scale processes (non-neutrality, Larmor radius).
[1, 2, 22, 24]. Thus, negative triangularity could provide an elegant solution for power plant design, the plasma being able to be heated to reactor relevant condi- tions without the potential critical damages caused by ELMs. These observations have motivated the fusion community to intensify both the modelling and the ex- perimental efforts on the impact of negative triangularity on global confinement and power exhaust. Concerning global confinement, two decades of experiments realised on TCV have shown that negative triangularity leads to a substantial re- duction of the fluctuations consistent with the beneficial effect observed on energy confinement [4, 5, 10, 22, 24]. Gyrokinetic simulations (GENE [8, 24], GS2 , LORB5[10, 22]) have been able to reproduce qualitatively the results concerning the reduction of electron heat transport with negative triangularity. In particu- lar, these simulations have shown that this reduction was linked, at least partly, to the stabilizing influence of negative triangularity on the trapped electron mode (TEM). In contrast, concerning the impact of triangularity on the power exhaust problematic, very few studies have been carried out despite its fundamental im- portance for tokamak viability. One of them concerns the impact of upper trian- gularity δ up on scrape-off layer power fall-off length λ q in a divertor configuration
of ﬁrst importance to validate our model. In order to do so, we presented the results of an experiment performed at JLF-Titan, before this thesis, side by side with the post- processed results of FCI2 simulations corresponding to each shot. The comparison of electron density measurements remained unfruitful. Yet, it has been reminded that both the diagnostic and the simulation have diﬀerent validity domains, whose overlap was very limited. The polarimetry measurement showed that no magnetic ﬁeld could be measured within the low density part of the plasma, in agreements with the post-processed result, showing a signiﬁcant rotation of the polarization only in the dense part of the plasma. Much attention was spent on the proton radiography diagnostic. After presenting the two methods used to generate the MeV protons (imploded backlighter on Omega, and the TNSA with short pulse laser in our case), we performed a sensitivity study of the diagnostic using ILZ, an ion trajectography code, and simple magnetic ﬁeld topologies. It showed that the variations of proton dose depend on the radial variations of the magnetic ﬁeld, and that for a thin enough disk of magnetic ﬁeld, the dose modulations are function of the magnetic ﬁeld integrated along the proton direction, ´ B.dz. Following, we continued this study by comparing the results of diﬀerent post-processed FCI2 simulations. It showed that for protons’ energies higher than 10 MeV, the results do not vary signiﬁcantly, including the case where the laser energy is varied. We showed that while changing the shape of the focal may aﬀect the result, the diagnostic may not be able to discriminate too small variations (such as ﬂat-top or super-Gaussian). Finally, this study showed the importance of the scattering when using proton radiography to probe solid targets. As such, we deﬁned the uncertainty on the measurement as a function of the scattering. Finally, the results of proton radiography exhibit a pattern of dose variation showing a ring of accumulation. Hence, in order to compare the post-processed and measured results as a function of time, we plotted the radius of the accumulation ring as a function of time, for both targets (low and high Z) and both the measurements and the simulations. It showed that the post-processed FCI2 simulations, using the NLSH model, were able to reproduce the measurement, all along the laser irradiation of the target.
The question of input estimation is not only related to plasma heat transport but arises more generally in fault detection and inverse problems.
This paper is organized as follows. The electron heat transport model and the framework of our PDE problem are presented in Section II. In Section III, we treat the diffusion and source term identifiability conditions. The adaptive estimators for functional (spatially varying) and distributed time-varying state, input and parameters are considered in Section IV. In order to illustrate the perfor- mance of the proposed identifiers, computer simulations are carried out in Section V.
Other analyses based on a more global approach of the drift wave equations for electrons and ions are finding that both mechanisms, curvature pinch and thermodiffusion, are inducing a particle pinch. For example, an analytical approach of the linear drift kinetic equation is presented in , 2D simulations in , computed particle trajectories in [mis], quasi-linear approach in  and 3D fluid model with a complementary analytical analysis in . These more global approaches show that the curvature particle pinch is always directed inward, but that the “thermodiffusion” term can either be directed inward when Ion Temperature Gradient modes (ITG) are dominant and outward when TEM are dominant. In particular, the curvature pinch mechanism presented in  can be recovered in the limit of small electron pressure fluctuations, i.e in the case where trapped electrons behave as “test particles” in turbulence mainly due to ion modes . These various effects are illustrated on figure 1 from  where the density profiles are the results of microturbulence simulations where the flux is fixed rather than the gradient. The particle flux is thus maintained to zero so that any density peaking is the signature of a turbulent pinch. If only the curvature terms are taken into account, a peaked profile is observed. Then when the thermodiffusion mechanism is implemented, the impact on the profile varies strongly with the ratio of electron heating versus ion heating, P e /P i . When P e /P i = 1, the density profile is similar to the curvature only
electrons can be accelerated with plasma up to several GeV within ultra-short distances [14–16] with kA peak curren- t, ultra-short bunches, 1π mm.mrad normalized emittance beams, enabling to consider LPA to drive an FEL [3, 17]. Even though some LPA features such as peak current and emittance seem to be quite suitable for the FEL application, energy spread and divergence do not meet conventional ac- celerator µrad divergence and per mille of energy spread beams. They should be handled to mitigate chromatic effect- s [18, 19], that can lead to a dramatic emittance growth and afferent beam quality degradation in the transfer lines. Large divergence requires strong focusing right after the electron source, with for instance high gradient permanent magnet quadrupoles . Large energy spread can be managed by a decompression chicane [3,21] or a transverse gradient undu- lator [22,23]. The energy-position correlation introduced by the chicane  can be turned into an advantage. There are still very few experiments with LPA electron beam transport towards an undulator  and preliminary observation of undulator radiation [25–28]. The COXINEL program  aiming at demonstrating FEL amplification using a dedi- cated manipulation line is developed in the frame of the LUNEX5 project of advanced compact free electron laser demonstrator [30, 31]. We report here the progress on the COXINEL experimental program.
A bigger picture starts to emerge, summarized in Table I , in which self-organization is present at all scales yet mani- fests itself differently at different scales; its most prominent feature being arguably the dynamical emergence of the me- soscale ⌬: at scales smaller than ⌬, transport is scale- invariant, avalanche-mediated, nonlocal and nondiffusive; at scales larger than ⌬, few genuinely scale-free avalanches ex- ist; rather, strongly coherent and persistent flows organize the turbulence into a jetlike pattern, the E ⫻B staircase. The sys- tem may thus either be seen as scale-invariant, nonlocal, nondiffusive 共fractal or self-similar兲 on some scale or, equivalently, strongly organized on some other. Further dis- FIG. 2. 共Color online兲 The “influence length” ⌬ is compared to
momentum so that a large gradient is needed for high energies. In the case of an LPA beam, a typical gradient of > 100 T/m is required. The conventional focusing magnets are electro-magnet based quadrupoles providing an intermediate gradient and wide tunability. However, the device has to be compact in order to achieve a high gradient which poses a mechanical complexity. Superconducting magnets come in handy for such applications but they are much more expensive than the conventional electro-magnets due to the cryogenic cost (installation and operation) and the possibility of a quench as a result of heating originating from synchrotron radiation and image charges. Permanent magnet based quadrupoles eliminate the need for power supplies, cables and the large element of infrastructure for the water cooling system and can be reduced in size without losing the magnetic field strength making them suitable for compact applications such as LPA [ 23 ].
4. One Dimensional Nanostructures
1D-NS used in photovoltaics, taking the form of familiar structures such as rods, tubes, and wires, possess two dimensions of a size between 1 and 100 nm while the third dimension is typically in the range 200 nm–1 µm. A wide variety of top-down and bottom-up fabrication approaches exist for their synthesis, with varying degrees of complexity that allow for greater or lesser control over the final structure. Chemical synthesis strategies for 1D-NS are often the cheapest and least demanding in terms of deposition equipment, and include electrodeposition, sol–gel synthesis, solvothermal methods, and electrochemical anodization. While ease of fabrication and relatively high-throughput make these methods attractive options, they often suffer from the drawback of having a greater variability in final properties due to the indirect measures of control inherent to these methods. Strategies based on physical or physicochemical synthesis of 1D-NS such as vapor phase deposition, chemical vapor deposition, vapor-liquid-solid growth, and atomic layer deposition often result in superior electronic properties due to lower impurities and superior crystallinity while requiring dedicated deposition equipment and extreme conditions such as high vacuum and/or elevated temperatures. Even more precise control over the final structure can be obtained by techniques such as electron beam lithography or focused-ion beam writing or x-ray lithography, although these processes are much more expensive and of low-throughput.
Combined distributed parameters and source estimation in tokamak plasma heat transport
Sarah Mechhoud 1 , Emmanuel Witrant 1 , Luc Dugard 1 and Didier Moreau 2
Abstract— : We investigate the joint estimation of time and space distributed parameters and input in the tokamak heat transport equation. This physical phenomenon can be modelled by a non-homogeneous linear parabolic partial differential equation (PDE). The analysis of this PDE is achieved in a finite dimensional framework using the cubic b-splines finite element method. The application of the parameter projection method results in a linear time-varying state-space model with unknown parameters and inputs. The DAISYS method proves the structural identifiability of the model and the EKF-UI-WDF estimates simultaneously the states, parameters and inputs. This methodology is applied on the tokamak plasma heat transport equation in order to reconstruct simultaneously its coefficients and its source term. Computer simulations on both mock-up and real data show the performance of the proposed technique.
Despite our initial conditions being oversimplified and not directly tied to any specific physical injection mechanism, we are encouraged by the close resemblance of sim.A’s results to MMS data. That this resemblance holds not only during the onset of the first reconnection events in sim.B, but also during the fully developed turbulent state, is particularly convincing. We are then led to conjecture that energy injection occurring near ion-kinetic scales, perhaps due to velocity-space instabilities and/or shocks, can qualitatively alter the evolution of CSs and the dynamics of magnetic reconnection inplasma turbulence, potentially explaining the MMS results. In particular, if some energy-injection mechanism with properties similar to those employed in our simulations occurs past the bow shock, our results suggest that e-rec events could be detected relatively close to the bow shock and also further downstream in the magnetosheath. A more recent observational study using an extended MMS data set from the turbulent magnetosheath [ 70 ] seems to support this scenario. As the MMS mission goes on, the amount of collected data will enable a more detailed statistical analysis of these e-rec events. This kind of analysis should include also data collected outside of the magnetosheath, in the pristine solar wind, where different statistics for the reconnecting current sheets may be expected. However, due to the different level of fluctuations in the two regions, we stress that a high sensitivity of the spacecraft’s instruments may be required in order to detect (the presumably smaller amount of) e-rec events in the pristine solar wind. Next-generation space missions would be most informative.
Abstract. The linear stability of chains of magnetic vortices in a plasma is investigated analytically in two dimensions by means of a reduced fluid model assuming a strong guide field and accounting for equilibrium electron temperature anisotropy. The chain of magnetic vortices is modelled by means of the classical "cat’s eyes" solutions and the linear stability is studied by analysing the second variation of a conserved functional, according to the Energy-Casimir method. The stability analysis is carried out on the domain bounded by the separatrices of the vortices. Two cases are considered, corresponding to a ratio between perpendicular equilibrium ion and electron temperature much greater or much less than unity, respectively. In the former case, equilibrium flows depend on an arbitrary function. Stability is attained if the equilibrium electron temperature anisotropy is bounded from above and from below, with the lower bound corresponding to the condition preventing the firehose instability. A further condition sets an upper limit to the amplitude of the vortices, for a given choice of the equilibrium flow. For cold ions, two sub-cases have to be considered. In the first one, equilibria correspond to those for which the velocity field is proportional to the local Alfvén velocity. Stability conditions imply: an upper limit on the amplitude of the flow, which automatically implies firehose stability, an upper bound on the electron temperature anisotropy and again an upper bound on the size of the vortices. The second sub-case refers to equilibrium electrostatic potentials which are not constant on magnetic flux surfaces and the resulting stability conditions correspond to those of the first sub-case in the absence of flow.
open-ended. In the proposed experiment, the positrons are produced by passing the electron bunches through a high-Z foil which blocks the upstream plasma flow. Thus, there will be no density ramp at the plasma entrance. At the plasma exit, however, the wake wavelength increases as the drive electron beam traverses the down-ramp. Since both the drive bunch and the accelerating positron bunch propagate at the speed of light, the relative spacing between them remains constant and the positrons enter the ion-rich body of the elongating wake and experience a defocusing transverse electric field. This transverse field strongly defocuses the positron beam into a ring as the accelerated positrons pass through the region where down-ramp exists. The positron beam exiting the plasma will therefore not be
The results presented in this thesis is the outcome of collective work of many team members. Most of the credits definitely go to Jérôme Faure, whose expertise and diligence led to a very well designed project with clear path and objectives to work on. His high quality standards permitted having an output of several international level publications that may be found at the back of this book, and patience discussing various physical aspects left the author of this manuscript as well as the other group members with few knowledge loopholes on how to aim for this quality. Secondly, nothing would have been possible without a long-term dedication and leadership by Rodrigo Lopez-Martens, whose team has for many years been devotedly developing the state-of-the-art laser system used in all the described experiments, introducing numerous highly innovative solutions on the way. Of greatest importance has been Aline Vernier, the main person behind putting the ideas of the two group leaders work in practice, always in the most clean and elegant way. Her efforts have made the setup as convenient to operate as possible, and her multi-skillfulness helped to overcome many unexpected obstacles of various sorts during the project. Diego Guénot has been the main driver of experimental execution during the first half of this thesis, when the most important breakthroughs were achieved. However, among the intense moments of fixing the never-ending final bugs he has always found time to teach the newly-arrived author the very basics of optics laboratory skills, which eventually permitted successful continuation with less human resources after his departure. Benoit Beaurepaire, the first PhD student of the project, delivered a lot of first hardware design and preliminary plasma acceleration studies, without which the later push to a higher maturity output could not have happened. Crucial has also been the major laser system upgrade by Frederik Böhle, whose hands were later just as well replaced by Marie Ouillé. The implementation of the CEP control tool by her together with Stefan Hässler allowed obtaining one of the most interesting sets of experimental data presented in this manuscript. A lot of troubles have been avoided by using microstructured plasma targets suggested and provided by François Sylla from SourceLab. Finally, it was a great pleasure to receive a lot of attention and input from Agustin Lifschitz, one of the best experts of numerical studies in the field, bringing a significantly clearer perspective into interpreting our results.