Editing Magnetic sail (section)

=== General kinematic model ===<!-- DM: Stopped detailed editing here 10/29/2023. -->

When the [[#MHD applicability test|MHD applicability test]] of <math display="inline">r_g/L</math> <1 then a kinematic simulation model more accurately predicts force transferred from the plasma wind to the spacecraft. In this case the effective sail blocking area <math>A_e</math> < <math>S=\pi L^2</math>.
[[File:Magnetic dipole force MHD and kinematic models.jpg|thumb|upright=1.5|Magnetic dipole force: MHD and kinematic models]]
The left axis of the figure is for plots of magnetic sail force versus characteristic length <math>L</math>.  The solid black line plots the MHD model force <math>F_{MHD} </math> from equation {{EquationNote|MHD.3}}. The green line shows the value of ion gyroradius <math>r_g \approx</math> 72&nbsp;km at 1 AU from equation {{EquationNote|MHD.5}}. The dashed blue line plots the hybrid MHD/kinematic model from equation {{EquationNote|MHD.6}}  from Fujita04.<ref name=":34" /> The red dashed line plots a curve fit to simulation results from Ashida14.<ref name=":25">{{Cite journal |last1=Ashida |first1=Yasumasa |last2=Yamakawa |first2=Hiroshi |last3=Funaki |first3=Ikkoh |last4=Usui |first4=Hideyuki |last5=Kajimura |first5=Yoshihiro |last6=Kojima |first6=Hirotsugu |date=2014-01-01 |title=Thrust Evaluation of Small-Scale Magnetic Sail Spacecraft by Three-Dimensional Particle-in-Cell Simulation |url=https://arc.aiaa.org/doi/10.2514/1.B35026 |journal=Journal of Propulsion and Power |volume=30 |issue=1 |pages=186–196 |doi=10.2514/1.B35026|hdl=2433/182204 |hdl-access=free }}</ref> Although a good fit for these parameters, the curve fit range of this model does not cover some relevant examples. Additional simulation results from Hajiwara15<ref>{{Cite web |last=Hajiwara |first=Tatsumasa |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=July 20, 2022 |website=electricrocket.org |location=Hyogo-Kobe, Japan}}</ref> are shown for the MHD and kinematic model as single data points as indicated in the legend. These models are all in close agreement. The kinematic models predict less force than predicted by the MHD model. In other words, the fraction <math>T_{loss}</math>  of thrust force predicted by the MHD model is lost when <math>r_g/L<1</math> as plotted on the right axis. The solid blue and red lines show <math>T_{loss}</math> for Fujita04<ref name=":34" /> and Ashida18<ref name=":25" /> respectively, indicating that operation with <math>L</math> less than 10% of <math>r_g</math> will have significant loss. Other factors in a specific magnetic sail design may offset this loss for values of <math>L<r_g</math>.<!-- Expand to further summarize Ashida18 PIC results at electron inertial scale. -->