Most of the artificial low-pressure plasmas contact with physical walls in laboratories; the plasma loss at the wall significantly affects the plasma device performance, e.g., an electric propulsion device. Near the surface of the wall, ions are spontaneously accelerated by a sheath and deliver their momentum and energy to the wall, while most of the electrons are reflected there. The momentum flux of the ions is a vector field, i.e., having both the radial and axial components even if the azimuthal components are neglected in a cylindrical system. Here the spatially-and vector-resolved measurement of the momentum flux near the cylindrical source wall of a magnetic nozzle radiofrequency (rf) plasma thruster configuration is successfully demonstrated by using a momentum vector measurement instrument. The results experimentally identify the spatial profile of a non-negligible axial momentum flux to the wall, while the radially accelerated ions seem to be responsible for the energy loss to the wall. The spatial profiles of the radial and axial momentum fluxes and the energy lost to the wall are significantly affected by the magnetic field strength. The results contribute to understand how and where the momentum and energy in the artificial plasma devices are lost, in addition to the presently tested thruster. The plasma momentum is one of the fundamental physical quantities associated with static and dynamic phenomena of plasmas in nature and laboratories. The energy flux being a scalar quantity can be given by the magnitude of the velocity, while the momentum flux is a vector quantity in general. It is crucial to understand and characterize the momentum transport, conversion, gain, and loss mechanisms for clarifying the structural formation of plasmas such as the astrophysical jets 1 , the particle acceleration in auroras at the Earth and Jupiter 2,3 , the coronal mass ejection from the Sun 4 , the interaction between the plasmas and the geomagnetic field 5 , and so on. In these naturally appearing plasmas, the processes involving the momentum and energy transfer occur due to the interaction with electromagnetic fields, collisions, turbulences, and so on, since they cannot see any physical boundaries in space except for the surface of planets. Terrestrial artificial plasmas ubiquitously contact to physical boundaries; forming a sheath maintaining charge balance in plasmas 6. Plasma-wall interactions involving the momentum transfer and loss also significantly affect the plasma behavior in the laboratories, e.g., in ref. 7,8 , in addition to the interactions occurring in the above-mentioned natural plasmas, e.g., interaction with the magnetic fields 9-11. The electric field perpendicular to the physical boundary is spontaneously formed in the sheath and accelerates the ions toward the boundary; resulting in the transfer of the momentum flux perpendicular to the surface. However, if they have velocity components parallel to the boundary surface, they can also deliver their momentum parallel to the boundary. Therefore,...

Spatial profiles of axial and radial momentum fluxes of a plasma expanding in a magnetic nozzle is revealed by using a momentum vector measurement instrument located downstream of a radiofrequency plasma source, where the radial and axial forces exerted to the detector plate facing the source side are independently, directly, and simultaneously obtained. It is shown that a conical structure having high electron temperature and plasma density is significantly responsible for the axial momentum flux, which corresponds to the thrust in an electric propulsion device. The radially outward momentum flux is detected at the outer region of the conical structure, where the electron pressure gradient is formed; implying that the ions are radially accelerated by an electric field. The increase in the radially integrated axial momentum flux along the axis is demonstrated, where the gain of the axial momentum flux occurs at the radially peripheral region of the plasma expanding along the magnetic nozzle.

Momentum vector measurement instrument yielding individual and simultaneous identification of local fluxes of momentum components in two different directions, i.e., vector-resolved force, is developed for understanding momentum transport in plasmas and the thrust generation mechanisms of a helicon plasma thruster. A detector plate is attached to a rotational arm connected to a pivot, which has a structure accessible to the inside of the thruster and is mounted on an axially movable balance structure. Simultaneous measurements of displacements of the rotational arm and the axially movable balance give the fluxes of the two different components of the momentum flowing into the detector surface, respectively, e.g., the radial and axial components. The detailed calibration results and the displacement signals induced by applying known forces in a bench test are shown. The results show that the presently developed technique gives resolutions of about 10 μN in the two different directions independently.

The profiles of the axial and radial momentum fluxes lost to the radial wall are experimentally investigated in a helicon source by using a momentum vector measurement instrument, where two gas injection configurations from the upstream of the source tube and from the downstream open source exit are tested. It is observed that the axial position of the maximum density is shifted to the source exit side for the downstream gas injection, compared with the upstream one. The measurement shows that the axial momentum flux transferred to the radial wall for the upstream gas injection is larger than that for the downstream gas injection, indicating that the axially accelerated ions are lost to the source wall. It is demonstrated that the loss of the axial momentum can be reduced by injecting the neutral gas near the open source exit, i.e., for the downstream gas injection.

Axial and radial momentum fluxes near a lateral wall in a helicon plasma source are preliminarily investigated by installing a momentum vector measurement instrument, which has a detector plate mounted on a double-pendulum structure movable in both the axial and radial directions. The result demonstrates the presence of the axial momentum flux transferred to the radial wall, which seems to be delivered by the ions having the axial velocity and lost to the wall. Furthermore, a significantly greater radial momentum flux is lost to the radial wall, implying that the energy loss occurs at the radial wall. The presently shown technique would be useful for identifying the spatial profile of the momentum vector of the plasma.The momentum flux of plasmas is one of the crucial physical quantities associated with acceleration, transport, and confinement of various plasmas [1][2][3][4], since many of the plasma characteristics are well described by momentum equations, which imply that the external forces applied to fluids are balanced to their momentum flux. Therefore, the momentum balance is very often used to model various plasmas ranging from naturally occurring plasmas to artificially-made terrestrial plasmas in small laboratories.One of the direct applications of the plasma momentum flux is an electric propulsion for spacecrafts [5]. The performance of the propulsion devices can be typically characterized by a thrust-to-power ratio F/P, a specific impulse I sp , and a thruster efficiency η p , where F and P are the thrust and the electric power, respectively [6]. The latter two are defined aswhere m dot and g are the mass flow rate of the propellant and the gravitational acceleration at sea level, respectively. Since all of the assessment parameters are given by the thrust F and the well-controlled parameters such as the electric power P and the mass flow rate m dot , the measurement of the thrust F should be taken on top priority to assess the thruster performance in laboratories. According to a momentum conservation of the spacecraft and the exhausted propellant, the thrust force is equal in magnitude and opposite in direction to the momentum flux exhausted from the spacecraft as well known as a rocket equation [6]. Therefore, the direct measurement of the thrust is indeed equivalent to the identification of the absolute value of the total momentum flux of the plasma; being also useful for understanding other plasmas if the local momentum flux can be identified.The direct and individual measurements of the total thrust and thrust components exerted to the axial wall, the radial wall, and the magnetic nozzle have clarified many aspects of physics in a magnetic nozzle helicon plasma thruster [7][8][9][10][11][12][13][14][15]. In highly ionized conditions, e.g., for propellants of xenon and krypton, or for several kW rf power in argon, the axially negative force on the radial wall, which directs to the downstream side and is integrated over the whole inner surface, has been detected in the individual measurement of the ...