Editing Magnetic sail (section)

=== Mini-magnetospheric plasma propulsion (M2P2) ===
[[File:Winglee M2P2 schematic.jpg|thumb|upright=1.5|Winglee M2P2 schematic]]
In 2000, Winglee, Slough and others proposed a design order to reduce the size and weight of a magnetic sail well below that of the [[#Magsail (MS)|magsail]] and named it mini-magnetospheric plasma propulsion (M2P2) that reported results adapted from a simulation model of the Earth's magnetosphere.<ref name=":2" /> The calculates speeds of 50 to 80&nbsp;km s−1 could enable spacecraft:<ref>Mini‐Magnetospheric Plasma Propulsion: Tapping the energy of the solar wind for spacecraft propulsion - Winglee - 2000 - [[Journal of Geophysical Research: Space Physics]]- Wiley Online Library</ref>

* To travel out of the solar system  
* To travel between the planets for low power requirements of ∼1&nbsp;kW per 100&nbsp;kg of payload and ∼0.5&nbsp;kg fuel consumption per day for acceleration periods of several days to a few weeks.

The figure based upon Winglee,<ref name=":2" /> Hajiwara,<ref name=":16">{{Cite web |last1=Hagiwara |first1=T. |last2=Kajimura |first2=Y. |last3=Oshio |first3=Y. |last4=Funaki |first4=I. |date=July 4–10, 2015 |title=Thrust Measurement of Magneto Plasma Sail with Magnetic Nozzle by Using Thermal Plasma Injection |url=http://electricrocket.org/IEPC/IEPC-2015-461p_ISTS-2015-b-461p.pdf |access-date=June 13, 2022 |website=}}</ref> Arita,<ref name=":17">{{Cite journal |last1=Arita |first1=H. |last2=Nishida |first2=H. |last3=Funaki |first3=I. |date=2014 |title=Magnetohydrodynamic Analysis of Thrust Characteristics on Magneto-Plasma Sail with Plasma Magnetic Field Inflation by Low-Beta Plasma |url=https://www.jstage.jst.go.jp/article/tastj/12/ists29/12_Pb_39/_pdf |journal=Trans. JSASS Aerospace Tech. Japan |volume=12 |issue=ists29 |pages=39–44 |doi=10.2322/tastj.12.Pb_39 |bibcode=2014JSAST..12.Pb39A |via=stage.jst.go.jp|doi-access=free }}</ref> and Funaki<ref name=":222" /> illustrates the M2P2 design, which was the basis of the subsequent [[#Magnetoplasma sail (MPS)|Magneto plasma sail (MPS)]] design. Starting at the center with a [[solenoid]] coil of radius <math>R_H</math> of <math display="inline">N_t</math>=1,000 turns carrying a radio frequency current that generates a [[Helicon (physics)|helicon]]<ref>{{Cite journal |last=Chen |first=Francis F. |date=May 1996 |title=Physics of helicon discharges |url=http://aip.scitation.org/doi/10.1063/1.871697 |journal=Physics of Plasmas |language=en |volume=3 |issue=5 |pages=1783–1793 |doi=10.1063/1.871697 |bibcode=1996PhPl....3.1783C |issn=1070-664X}}</ref> wave that injects plasma fed from a source into a coil of radius <math display="inline">R_c</math> that carries a current of <math>I_c</math>, which generates a magnetic field. The excited injected plasma enhances the magnetic field and generates a miniature magnetosphere around the spacecraft, analogous to the [[Heliosphere#Heliopause|heliopause]] where the Sun injected plasma encounters the interstellar medium, [[coronal mass ejection]]s or the Earth's [[Magnetosphere#Magnetotail|magnetotail]]. The injected plasma created an environment that analysis and simulations showed had a magnetic field with a falloff rate of <math>1/r</math> as compared with the classical model of a <math display="inline">1/r^3</math> falloff rate, making the much smaller coil significantly more effective based upon analysis<ref name=":27">{{Cite web |last=Slough |first=John |date=2001 |title=High Beta Plasma for Inflation of a Dipolar Magnetic Field as a Magnetic Sail |url=https://earthweb.ess.washington.edu/space/M2P2/iepc.slough.PDF |archive-url=https://ghostarchive.org/archive/20221009/https://earthweb.ess.washington.edu/space/M2P2/iepc.slough.PDF |archive-date=2022-10-09 |access-date=July 3, 2022 |website=earthweb.ess.washington.edu}}</ref> and simulation.<ref name=":2" /> The pressure of the inflated [[Plasma (physics)|plasma]] along with the stronger magnetic field pressure at a larger distance due to the lower falloff rate would stretch the magnetic field and more efficiently inflate a magnetospheric bubble around the spacecraft.

Parameters for the coil and solenoid were <math>R_H</math>=2.5&nbsp;cm and for the coil <math display="inline">R_c</math>= 0.1 m, 6 orders of magnitude less than the magsail coil with correspondingly much lower mass. An estimate for the weight of the coil was 10&nbsp;kg and 40&nbsp;kg for the plasma injection source and other infrastructure. Reported results from Figure 2 were <math>B_0 \approx</math> {{e|−3}} T at <math>R_{mp} \approx</math> 10&nbsp;km and from Figure 3 an extrapolated result with a plasma injection jet force <math display="inline">F_{jet} \approx</math>10<sup>−3</sup> N resulting in a thrust force of <math display="inline">F_{M2P2} \approx </math>  1 N. The magnetic-only sail force from equation {{EquationNote|MHD.3}} is <math>F_w</math>=3x10<sup>−11</sup> N and thus M2P2 reported a thrust gain of 4x10<sup>10</sup> as compared with a magnetic field only design. Since M2P2 injects ionized gas at a <math>m_{in}</math> [[Mass flow rate|mass flow rate (kg/s)]] it is viewed as a propellant and therefore has a ''[[specific impulse|specific impulse (s)]]'' <math>I_{sp}=F_{M2P2}/m_{in}/g_0</math> where <math>g_0</math> is the acceleration of [[Earth's gravity]].  Winglee stated <math>m_{in}</math>=0.5&nbsp;kg/day and therefore <math>I_{sp}</math>=17,621. The equivalent exhaust velocity <math>v_e=g_0 \, I_{sp}</math> is 173&nbsp;km/s for 1 N of thrust force. Winglee assumed total propellant mass of 30&nbsp;kg and therefore propellant would run out in 60 days.<ref name=":2" />

In 2003, Khazanov published [[Magnetohydrodynamics|MagnetoHydroDynamic]] (MHD) and kinetic studies<ref name=":9" /> that confirmed some aspects of M2P2 but raised issues that the sail size was too small, and that very small thrust would result and also concluded that the hypothesized <math display="inline">1/r</math> magnetic field falloff rate was closer to <math display="inline">1/r^2</math>. The plasma density plots from Khazanov indicated a relatively high density inside the magnetospheric bubble as compared with the external solar wind region that differed significantly from those published by Winglee where the density inside the magnetospheric bubble was much less than outside in the external solar wind region.

A detailed analysis by Toivanen and others in 2004<ref name=":8" /> compared a theoretical model of Magsail, dubbed Plasma-free Magnetospheric Propulsion (PFMP) versus M2P2 and concluded that the thrust force predicted by Winglee and others was over ten orders of magnitude optimistic since the majority of the solar wind momentum was delivered to the magnetotail and current leakages through the magnetopause and not to the spacecraft.<ref name=":15">{{Cite web |last=Janhunen |first=P. |date=October 11, 2002 |title=Comment on: "Mini-magnetospheric plasma propulsion: tapping the energy of the solar wind for spacecraft propulsion" by R. Winglee et al. |url=https://space.fmi.fi/~pjanhune/papers/winglee.pdf |archive-url=https://ghostarchive.org/archive/20221009/https://space.fmi.fi/~pjanhune/papers/winglee.pdf |archive-date=2022-10-09 |access-date=June 28, 2022 |website=space.fmi.fi}}</ref> Their comments also indicated that the magnetic field lines may not close near enough to the coil to achieve significant transfer of force. Their analysis made an analogy to the [[Heliospheric current sheet]] as an example in astrophysics where the magnetic field could falloff at a rate of between <math display="inline">1/r</math> and <math display="inline">1/r^2</math>. They also analyzed current sheets reported by Winglee from the magnetopause to the spacecraft in the windward direction and a current sheet in the magnetotail. Their analysis indicated that the current sheets needed to pass extremely close to the spacecraft to impart significant force could generate significant heat and render this leverage impractical.

In 2005, Cattell and others<ref name="05ja026_full" /> published comments regarding M2P2 that included a lack of magnetic flux conservation in the region outside the magnetosphere that was not considered in the Khazanov studies. Their analysis concluded in Table 1 that Winglee had significantly underestimated the required sail size, mass, and required magnetic flux. Their analysis asserted that the hypothesized <math display="inline">1/r</math> magnetic field falloff rate was not possible.

The expansion of the magnetic field using injected plasma was demonstrated in a large vacuum chamber on [[Earth]], but quantification of thrust was not part of the experiment.<ref>{{Cite web |last=Winglee |first=R.M. |date=November 2001 |title=Mini-Magnetospheric Plasma Propulsion (M2P2) NIAC Award No. 07600-032: Final Report |url=http://www.niac.usra.edu/files/studies/final_report/372Winglee.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.niac.usra.edu/files/studies/final_report/372Winglee.pdf |archive-date=2022-10-09 |access-date=July 7, 2022 |website=niece.usra.edu}}</ref> The accompanying presentation has some good animations that illustrate physical principles described in the report.<ref>{{Cite web |last1=Winglee |first1=R.M. |last2=Ziemba |first2=T. |last3=Slough |first3=J. |last4=Euripedes |first4=P. |date=June 2001 |title=Mini-Magnetic Plasma Propulsion [M2P2] |url=http://www.niac.usra.edu/files/library/meetings/annual/jun01/372Winglee.pdf |archive-url=https://ghostarchive.org/archive/20221009/http://www.niac.usra.edu/files/library/meetings/annual/jun01/372Winglee.pdf |archive-date=2022-10-09 |access-date=July 7, 2022 |website=niece.usr.edu}}</ref>  A 2004 Winglee paper focused on usage of M2P2 for electromagnetic shielding.<ref>{{Cite journal |last=Winglee |first=Robert |date=2004 |title=Advances in Magnetized Plasma Propulsion and Radiation Shielding |journal=Proceedings of the 2004 NASA.DoD Conference on Evolution Hardware |citeseerx=10.1.1.513.2375 }}</ref> Beginning in 2003, the [[#Magnetoplasma sail (MPS)|Magneto plasma sail]] design further investigated the plasma injection augmentation of the magnetic field, used larger coils<ref name=":20" /> and reported significantly more modest gains.