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therefore accounts as losses. An efficient magnetic nozzle is sufficiently long to minimize the amount of energy wasted in the radial and azimuthal directions. Additionally, an excessively weak magnetic field would fail to confine radially and guide axially the plasma, incurring in large radial losses.
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The efficiency of the magnetic nozzle has to be discussed in terms of divergence or radial losses. As a byproduct of the expansion in the divergent magnetic nozzle, part of the kinetic energy of ions is directed in the radial and azimuthal directions. This energy is useless for thrust generation, and
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The separation of ions due to their inertia leads to the formation of local longitudinal electric currents, that do not violate however the global current-free condition in the jet. The influence of the plasma-induced magnetic field, which can deform the magnetic nozzle downstream, and the formation
310:
velocities thanks to the role of the internal electric field in the plasma. Eventually, the unmagnetized, massive ions are fast enough that the weak electric and magnetic forces in the downstream region become insufficient to deflect the ion trajectories except for extremely high magnetic strengths.
68:
i.e. avoiding the material contact with the hot plasma, which would lead to system inefficiencies and reduced lifetime of the nozzle. Additional advantages include the capability of modifying the strength and geometry of the applied magnetic field in-flight, allowing the nozzle to adapt to different
298:
The closed nature of the magnetic lines means that unless the plasma separates from the guiding magnetic field downstream, it will turn around along the field lines back to the thruster. This would defeat the propulsive purpose of the magnetic nozzle, as the returning plasma would cancel thrust and
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In steady-state operation, the exhausted plasma jet is globally current-free, i.e., the total ion current and electron current at each section are equal. This condition prevents the continuous electrical charging of the spacecraft on which the magnetic nozzle is mounted, which would result if the
165:. As a result of the ensuing electric field, the ions are accelerated downstream, while all electrons except the more energetic ones are confined upstream. In this way, the electric field helps convert the electron internal energy into directed ion kinetic energy.
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that is actually deflected along the magnetic field and turns back to maintain quasineutral conditions in the plasma is negligible. In consequence, the magnetic nozzle is capable of delivering detached plasma jets usable for propulsion.
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The expansion of a plasma in a magnetic nozzle is inherently more complex than the expansion of a gas in a solid nozzle, and is the result of several intertwined phenomena, which ultimately rely on the large mass difference between
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device, whose role is to convert plasma thermal energy into directed kinetic energy as discussed above. Therefore, thrust and specific impulse are strongly dependent on the
236:
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of the plasma inside the plasma source. A high electron temperature (i.e., a hot plasma) is required to have an effective plasma thruster.
176:, which is proportional to the pressure of electrons and inversely proportional to the magnetic field strength. Together with the
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prevents the uncontrolled expansion of the electrons in the radial direction and guides them axially downstream. The heavier
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motion about the magnetic lines. In practice, this is achieved with magnetic fields in the range of a few hundred Gauss. The
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Other figures of merit of the system are the electric power, mass and volume of the required magnetic field generator (
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are typically unmagnetized or only partially magnetized, but are forced to expand with the electrons thanks to the
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forces acting on solid walls. The main advantage of a magnetic nozzle over a solid one is that it can operate
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depends on the plasma thruster to which it is connected. The magnetic nozzle should be regarded as a thrust
32:. The magnetic field in a magnetic nozzle plays a similar role to the convergent-divergent solid walls in a
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363:). A low electric power consumption, mass and volume are desirable for space propulsion applications.
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As the plasma expands in the divergent side of the magnetic nozzle, ions are gradually accelerated to
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As a natural consequence, plasma detachment starts to take place and, the amount of plasma
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to this force is felt on the magnetic generator of the magnetic nozzle and is called
73:. Magnetic nozzles are the fundamental acceleration stage of several next-generation
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mechanism is therefore necessary for the correct operation of the magnetic nozzle.
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The electron pressure being confined by the magnetic field gives rise to a
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Plasma detachment in a propulsive magnetic nozzle via ion demagnetization,
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could endanger the integrity of the spacecraft and the plasma thruster. A
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Plasma
Sources Science and Technology, Vol. 25, No. 4, 2016, pp. 045012.
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Plasma
Sources Science and Technology, Vol. 23, No. 3, 2014, pp. 032001.
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of non-neutral regions, can further reduce the turn-back plasma losses.
93:. Magnetic nozzles also find another field of application in advanced
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Two-dimensional supersonic plasma acceleration in a magnetic nozzle,
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in the plasma domain. This azimuthal electric current generates an
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of each electron is forced to travel along one magnetic tube. This
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Effect of the plasma-induced magnetic field on a magnetic nozzle,
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If the strength of the applied magnetic field is sufficient, it
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processes, and their physics are related to those of several
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amount of ions and electrons emitted per unit time differ.
48:. Like a de Laval nozzle, a magnetic nozzle converts the
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Characterization of plasma flow through magnetic nozzles
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The performance of a magnetic nozzle, in terms of its
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which opposes the applied one, generating a repulsive
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Physics of
Plasmas, Vol. 18, No. 5, 2011, pp. 053504
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On plasma detachment in propulsive magnetic nozzles,
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R.A. Gerwin, G.J. Marklin, A.G. Sgro, A.H. Glasser,
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130:interactions between them and the applied field.
379:Andersen et al. Physics of Fluids 12, 557 (1969)
36:, wherein a hot neutral gas is expanded first
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91:applied-field magnetoplasmadynamic thruster
141:in the plasma, which therefore describe a
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161:that is set up in the plasma to maintain
77:currently under development, such as the
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278:that pushes the plasma downstream. The
24:that guides, expands and accelerates a
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413:Physics of Plasmas 17, 073501 (2010)
271:{\displaystyle \propto j_{\theta }B}
109:Basic operation of a magnetic nozzle
28:jet into vacuum for the purpose of
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395:, LANL report AL-TR-89-092 (1990)
60:in the plasma, rather than on
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83:electron-cyclotron resonance
69:propulsive requirements and
52:of the plasma into directed
288:thrust generation mechanism
231:{\displaystyle j_{\theta }}
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20:is a convergent-divergent
195:{\displaystyle E\times B}
448:Merino, M., Ahedo, E.,
435:Merino, M., Ahedo, E.,
422:Ahedo, E., Merino, M.,
79:helicon plasma thruster
324:Propulsive performance
290:in a magnetic nozzle.
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240:induced magnetic field
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409:E. Ahedo, M. Merino,
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85:plasma thruster, the
346:electron temperature
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151:magnetic confinement
99:magnetic confinement
95:plasma manufacturing
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474:Rocket propulsion
361:permanent magnets
301:plasma detachment
294:Plasma detachment
286:This is the main
174:diamagnetic drift
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30:space propulsion
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163:quasineutrality
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50:internal energy
34:de Laval nozzle
18:magnetic nozzle
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244:magnetic force
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159:electric field
147:guiding center
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71:space missions
66:contactlessly,
54:kinetic energy
42:supersonically
22:magnetic field
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44:to increase
38:subsonically
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463:Categories
367:References
338:efficiency
308:hypersonic
207:azimuthal
143:helicoidal
137:the light
135:magnetizes
89:, and the
469:Magnetism
261:θ
253:∝
224:θ
187:×
139:electrons
116:electrons
105:devices.
40:and then
280:reaction
128:magnetic
124:electric
122:and the
62:pressure
359:and/or
101:plasma
334:thrust
103:fusion
87:VASIMR
81:, the
46:thrust
26:plasma
203:drift
155:ions
126:and
120:ions
118:and
465::
400:^
384:^
16:A
266:B
257:j
220:j
190:B
184:E
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