Editing Magnetic sail (section)

==== Coil mass and current (CMC) ====

The minimum required mass to carry the current in equation {{EquationNote|MS.1}} or other magnetic sail designs from Andres/Zubrin (9)<ref name=":13" />{{Rp|location=Eq (9)}} and Crowl<ref name=":29">{{Cite web |last=Crowl |first=Adam |date=September 2017 |title=High-Speed Magnetic-Sail Interstellar Precursor Missions Enabled by Metastable Metallic Hydrogen |url=https://www.researchgate.net/publication/321110213 |access-date=August 14, 2022 |work=68th International Astronomical Conference |location=Adelaide Australia}}</ref>{{Rp|location=Eq (3)}} as follows:{{NumBlk2|:|<math>_{min}M_c \, = 2 \, \pi \, R_c \, I_c \, / (J _e/ \delta_c)</math>|CMC.1}}

where <math>J_e</math> is the superconductor critical [[Current density|current density (A/m<sup>2</sup>)]] and <math display="inline">\delta_c</math> is the coil material density, for example <math>J_e</math> = 1x10<sup>11</sup> A/m<sup>2</sup> and <math display="inline">\delta_c</math> = 6,500&nbsp;kg/m<sup>3</sup> for a superconductor in Freeland<ref name=":14" />{{Rp|location=Apdx A}} The physical mass of the coil is

{{NumBlk2|:|<math>_{phy}M_c= (2 \, \pi  +N_{tether} ) \, R_c  \, \pi \, r_c^2 \, \delta_c</math>|CMC.2}}

where <math>r_c </math> is the radius of the superconductor wire, for example that necessary to handle the tension for a particular use case, such as deceleration in the ISM where  <math>r_c </math> = 10&nbsp;mm.<ref name=":14" />{{Rp|location=Apdx A}}  The <math>N_{tether}</math> factor (e.g., 3) accounts for mass of the tether (or shroud) lines to connect the coil to a spacecraft. Note that <math>_{phy} M_c</math> with <math>N_{tether}</math>=0 must be no less than <math>_{min}M_c</math> in order for the coil to carry the [[Superconductivity#Elementary properties of superconductors|superconductor critical current]] <math>I_{cc}=J_e \pi r_c^2</math> amperes for a coil wire of radius <math>r_c</math>, for example <math>I_{cc}</math> = 7,854 [[Kiloampere|kiloampere (kA.)]]<ref name=":14" />{{Rp|location=Apdx A}}

Setting equation {{EquationNote|CMC.2}} with <math>N_{tether}</math>=0 equal to equation {{EquationNote|CMC.1}} and solving for <math>r_c</math> yields the minimum required coil radius

{{NumBlk2|:|<math>_{min} r_c =\sqrt{I_c/(J_e \pi)}
</math>|CMC.3}}

If operated within the solar system, high temperature [[superconducting wire]] (HTS) is necessary to make the magsail practical since required current is large, millions of amperes. Protection from solar heating is necessary closer to the Sun, for example by highly reflective coatings.<ref>{{Cite journal |last1=Youngquist |first1=Robert C. |last2=Nurge |first2=Mark A. |last3=Johnson |first3=Wesley L. |last4=Gibson |first4=Tracy L. |last5=Surma |first5=Jan M. |date=2018-05-01 |title=Cryogenic Deep Space Thermal Control Coating |url=https://arc.aiaa.org/doi/10.2514/1.A34019 |journal=Journal of Spacecraft and Rockets |volume=55 |issue=3 |pages=622–631 |doi=10.2514/1.A34019 |bibcode=2018JSpRo..55..622Y |issn=0022-4650}}</ref> If operated in interstellar space low temperature superconductors (LTS) could be adequate since the temperature of a vacuum is 2.7{{nbsp}}[[Kelvin|Kelvins (K)]], but radiation and other heat sources from the spacecraft may render LTS impractical. The critical current <math>I_{cc}</math> of the [[Superconducting wire#Coated superconductor tape or wire|HTS YBCO coated superconductor wire]] increases at lower temperatures with a current density <math>J_e</math> of 6x10<sup>10</sup> A/m<sup>2</sup> at 77{{nbsp}}K and 9x10<sup>11</sup> A/m<sup>2</sup> at 5{{nbsp}}K.