## 2 Multi-Mode MEICP Reactors Theoretical Background  
The next-generation of LEO solar-powered spacecraft imposes extended control capabilities, including initial orbit and final orbit insertion, phasing, and station keeping, followed by orbit maintenance, re-phasing, and attitude control. A HPT based on MEICP reactors and the MN acceleration scheme is engineered to provide a versatile operational envelope based on MEICP reactors and the MN acceleration scheme for the future commercialization of both LEO and VLEO orbits. This flexibility supports both short pulses and steady-state operation, with magnetic fields that closely replicate the optimal conditions for helicon-wave excitation. To develop compact EP systems based on a fully electrodeless architecture, it is essential to have a comprehensive understanding of the wave-plasma coupling mechanisms and their synergistic relationships with propulsion metrics and plasma parameters. Low-frequency whistler waves, commonly known as helicon waves, appear within a distinct area of the Clemmow-Mullaly-Allis (CMA) diagram. This particular region is defined by an operational frequency \((\omega)\) that lies between the lower hybrid frequency \((\omega_{LH})\) and the electron-cyclotron frequency \((\omega_{ce})\) while remaining much lower than the plasma frequency [31]. The operation of the HPT is analyzed through a self-consistent model that integrates power balance, particle balance, and the structure of the RF field. In the MEICP reactor, power deposition is governed by the RF field structure, which is defined by the excited eigenmode. The operational resonance frequency is such that the eigenmode arises from electron response, irrespective of ions influence. When the helion waves propagate near resonance cone angle \(\left(\theta_{res}=cos^{-1}(\omega/\omega_{ce})\right)\)[32], plasma density peaks in the MEICP reactor. An RF-driven HPT using a HWRH antenna can generate right-rotating RF fields, causing free electrons to oscillate at a frequency dictated by the static magnetic field. A global model (GM) of RF-driven HPT, relying exclusively on energy and particle balance, has been proposed to predict the steady-state electron temperature and density as function of the input parameters [33]. Furthermore, this GM is not influenced by the specific plasma excitation methods and has been used in the preliminary design of the MEICP reactor. Nevertheless, the GM cannot foresee certain peculiarities of the helicon-heated plasmas, such as abrupt transitions between different modes, necessitating experimental validation. Using a helicon-pulsed excitation technique, the proposed RF-driven electric thruster exhibits distinct behaviors based on the power levels and density thresholds. The MEICP reactor performs in either Capacitively Coupled Plasma (CCP or, E-mode) or Inductively Coupled Plasma (ICP or H-mode) at low and medium power levels. At high power levels, above 500 W, the plasma reactor may transition to Wave Coupled Plasma(WCP), known as the helicon mode. One of the distinctive characteristics of argon MEICP source discharges is the mode transition, marked by a significant increase in electron density as RF power or magnetic field strength increases. The W-mode induction occurs in a capacitive E-mode due to the voltage drop across the azimuthally axisymmetric HWRH antenna. When exposed to moderate power, the reactor of the HPT transitions into an inductive H-mode [34; 35]. This is distinguished by the generation of an oscillating magnetic field in the antenna, which, in turn, induces the electric field that sustains the discharge. An optimal level of RF input energy is required to satisfy the dispersion relation of the helicon wave. This operating point is associated with a state of resonance when the wavelengths of the HWs match the demands for the cavity modes. At low plasma densities, the MEICP reactor is dominated, but beyond a certain plasma density threshold, the W-mode becomes dominant [11; 36].