Bernstein Greene and Kruskal (BGK) modes are nonlinear electrostatic undamped waves in collisionless plasmas which are exact solutions of the steady state Vlasov-Poisson equations Since the seminal paper by BGK numerous studies have been conducted for sixty years in theory space observations numerical simulations and laboratory experiments This is because waves that are considered BGK modes have been ubiquitously observed in nature (in space) regardless of its seemingly fragile structure in phase space A target of this study is the first direct measurement of phase space structures f (x v) of the phase space electron hole that is a type of BGK modes in laboratory magnetized plasmas where f x and v represent the electron distribution function coordinates of the physical space and the velocity space respectively Our idea to achieve the target is to apply a voltage-sweeping Langmuir probe (LP) at a fixed position into propagating periodic BGK modes having electron hole structures in the phase space which are generated by a chirped-frequency drive A fast voltage sweep of the LP enables to cover the phase space with a satisfactory time resolution f (x v) is obtained by Druyveteyn method with a digital differentiation of current-voltage curves measured by LP For this purpose we designed a fast voltage sweep LP (FVSLP) which consists of two probe channels including a dummy channel and a differential amplifier The dummy channel is employed for cancellation of the stray current induced by the fast voltage sweep After the development of the FVSLP we applied it to plasma experiments on electron-hole excitations with the use of the autoresonance technique in the magnetized plasma experiment (MPX) device The results of the FVSLP measurement in the BGK mode-excitation experiment in MPX indicated no clear evidence of emergence of a hole structure in the electron phase space during propagating of a pulse train of the excited waves One possible reason is that electron confinement time was shorter than the time duration of the external drive chirp i e the time necessary for production of bucket-electron holes In near future we improve the situation by increase in the chirp rate of the external drive and extension of the confinement time for generating BGK modes

Direct Measurement of Phase Space Structure of BGK Modes in Laboratory Magnetized Plasmas

云瑄, 張. (Author). 2016 Sep 7

Student thesis: Master's Thesis