The proposed thesis subject is : **advanced shaping of wave-particle interaction in traveling wave tubes**

Before addressing the details of this subject further down in the text, it is appropriate to specify for the attention of the candidates (F/M) the practical modalities of this thesis and of the preparation of the doctoral degree in which it is included.

This thesis is in the framework of a French PhD diploma, prepared at the doctoral school “Physics and Material Sciences” (ED252) of Aix-Marseille University. The start is planned for the fall of 2023. Half of the funding is provided by the French Centre National d’Etudes Spatiales (CNES) and the other half by the company Thales. For the successful candidate (F/M), it will take the form of a fixed-term employment contract called “doctoral contract” for a period of 3 years from 01/10/2023 to 30/09/2026. The employer would be the CNES and the thesis would take place at the PIIM laboratory in Marseille with regular travel to Thales in Velizy (Paris area). The selected candidate (F/M) would be consequently employed by CNES for 3 years, the work contract remaining conditioned by the continuation of the preparation of the PhD.

Thus, the applications will have to be, in due time, formalized with the CNES, on its application site, i.e. between 01/02/2023 and 15/03/2023 when the position is posted.

Before applying, it is **strongly recommended** to read very carefully the subject and then to contact **as soon as possible** by mail the future co-supervisors, Professor Yves Elskens (yves.elskens (at) univ-amu.fr) at the PIIM laboratory, and Frédéric André (frederic.andre (at) thalesgroup.com), research engineer at Thalesgroup (AVS Microwave and Imaging Systems).

This topic is also closely related to the internship offered at the laboratory from March to July 2023. It goes without saying that a successful internship on this topic finds its natural extension in the preparation of the PhD.

Thesis subject : **advanced shaping of wave-particle interaction in traveling wave tubes**

Wave-particle interaction is a fundamental process in the physics of hot and natural plasmas, accelerators and beams ; in particular, it is the basis of wave amplifiers such as free electron lasers, gyrotrons, traveling wave tubes… The power in some of these devices and their broad frequency spectrum lead to instabilities, nowadays increasingly critical and hard to simulate. A microscopic description enables a better understanding of the coupling mechanisms between N particles and the amplified radiofrequency waves using hamiltonian dynamics. For *N* → ∞, the dynamics of this system converges to the one described by vlasovian kinetic equations.

Numerical simulation currently relies on two types of models. Particle-in-Cell (PIC) models rest on a minimal simplification of physics equations but lead to huge computing times, as the number of degrees of freedom is very large. Specialized models, in contrast, allow simulating only particular regimes, but with outstandingly shorter times.

The very popular envelope model is a frequency-domain model in which the amplified wave is represented by the cold wave (the wave propagating in the absence of beams), multiplied with an envelope function varying with the position along the propagation direction. This frequency-domain approach is not fit for investigating nonlinear regimes, like saturation instabilities and intermodulation effects.

We developed a novel time-domain model with few degrees of freedom thanks to an efficient representation of fields, enabling a realistic simulation of amplification in traveling wave tubes. We shall confront these simulations with experiment in space traveling wave tubes and in the 4 metre long device which enabled our laboratory to perform the first direct observation of several fundamental processes of this physics.

The Ph.D. will focus on developing simple nonlinear models and using them numerically toward applications in particular to the traveling wave tubes of Thales Avionics (Vélizy) and in our laboratory (Marseille). Three specific research lines are being considered :

– adapting the current model (designed for uniform structures) to structures with space-dependent characteristics (tapers) ;

– describing more accurately the reflection processes at space-dependent defects ;

– investigating the operation of TWT with pulsed RF input (instead of permanent harmonic input) ; this pulsed regime may enable reachng much higher interaction efficiencies ; this physics is also relevant to other applications, aiming at accelerating particles using short pulses. A master degree internship is open with our team from March 2023.

References :

– Y. Elskens & D. Escande, Microscopic dynamics of plasmas and chaos (IoP Publishing, Bristol, 2003).

– F. André, P. Bernardi, N.M. Ryskin, F. Doveil & Y. Elskens, Hamiltonian description of self-consistent wave-particle dynamics in a periodic structure, Europhys. Lett. 103 (2013) 28004.

– D.F.G. Minenna, Y. Elskens, F. André & F. Doveil, Electromagnetic power and momentum in N-body hamiltonian approach to wave-particle dynamics in a periodic structure, Europhys. Lett. 122 (2018) 44002.

– Kh. Aliane, Y. Elskens, F. André & D.F.G. Minenna, Many-particle models and short pulse amplification in traveling wave tubes, IEEE Trans. El. Dev. 68 (2021) 6476-6481

– D.F.G. Minenna, Kh. Aliane, Y. Elskens, A. Poyé, F. André, J. Puech & F. Doveil, Time simulation of the nonlinear wave-particle interaction in meters long traveling-wave tubes, Phys. Plasmas 28 (2021) 092110

– PhDs in Marseilles : A. Macor (2007), A. Aïssi (2008), P. Bernardi (2011), S. Théveny (2016), D. Minenna (2019), Kh. Aliane (in progress).