Knot Probability of Random Magnetic Field Lines
In this paper, we apply several latest results from statistical physics on the probability and energy of knotting to study the knotted field lines in solar corona. Since the solar magnetic field in small scale can be seen as nearly random, by assuming that the magnetic field lines behave similarly t...
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| author | Anda Xiong Shangbin Yang Xin Liu |
| author_facet | Anda Xiong Shangbin Yang Xin Liu |
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| description | In this paper, we apply several latest results from statistical physics on the probability and energy of knotting to study the knotted field lines in solar corona. Since the solar magnetic field in small scale can be seen as nearly random, by assuming that the magnetic field lines behave similarly to random loops, we find the probability <i>P</i> of certain knot type <i>K</i> for the field line knotting as a function to the distance <i>L</i> between the foot-points of sunspots, which is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>P</mi><mi>K</mi></msub><mrow><mo>(</mo><mi>L</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>C</mi><mi>K</mi></msub><msup><mi>L</mi><mrow><mn>2</mn><msub><mi>α</mi><mi>K</mi></msub></mrow></msup><mo form="prefix">exp</mo><mrow><mo>(</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mo>−</mo><msup><mi>L</mi><mn>2</mn></msup></mrow><mi>β</mi></mfrac></mstyle><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. From the equation, we find that the variety of knot type increases with the distance. Since knotting is the topological resemblance to magnetic helicity, which is an invariant for ideal MHD, our result enriches the understanding of the probability of magnetic helicity as well as field line structure in active regions. Based on the relation between knotting and magnetic energy, we provide support to the high variety of field line knot types. |
| format | Article |
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| issn | 2218-1997 |
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| spelling | doaj-art-e5953863848b4e20b04c460126a1ad422025-08-20T03:13:54ZengMDPI AGUniverse2218-19972025-03-0111411010.3390/universe11040110Knot Probability of Random Magnetic Field LinesAnda Xiong0Shangbin Yang1Xin Liu2School of Systems Science, Institute of Non-Equilibrium Systems, Beijing Normal University, Beijing 100875, ChinaState Key Laboratory of Solar Activity and Space Weather, Beijing 100190, ChinaSchool of Physics and Optoelectronic Engineering, Beijing University of Technology, Beijing 100124, ChinaIn this paper, we apply several latest results from statistical physics on the probability and energy of knotting to study the knotted field lines in solar corona. Since the solar magnetic field in small scale can be seen as nearly random, by assuming that the magnetic field lines behave similarly to random loops, we find the probability <i>P</i> of certain knot type <i>K</i> for the field line knotting as a function to the distance <i>L</i> between the foot-points of sunspots, which is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>P</mi><mi>K</mi></msub><mrow><mo>(</mo><mi>L</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>C</mi><mi>K</mi></msub><msup><mi>L</mi><mrow><mn>2</mn><msub><mi>α</mi><mi>K</mi></msub></mrow></msup><mo form="prefix">exp</mo><mrow><mo>(</mo><mstyle scriptlevel="0" displaystyle="true"><mfrac><mrow><mo>−</mo><msup><mi>L</mi><mn>2</mn></msup></mrow><mi>β</mi></mfrac></mstyle><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. From the equation, we find that the variety of knot type increases with the distance. Since knotting is the topological resemblance to magnetic helicity, which is an invariant for ideal MHD, our result enriches the understanding of the probability of magnetic helicity as well as field line structure in active regions. Based on the relation between knotting and magnetic energy, we provide support to the high variety of field line knot types.https://www.mdpi.com/2218-1997/11/4/110knotsolar physicsmagnetic field |
| spellingShingle | Anda Xiong Shangbin Yang Xin Liu Knot Probability of Random Magnetic Field Lines Universe knot solar physics magnetic field |
| title | Knot Probability of Random Magnetic Field Lines |
| title_full | Knot Probability of Random Magnetic Field Lines |
| title_fullStr | Knot Probability of Random Magnetic Field Lines |
| title_full_unstemmed | Knot Probability of Random Magnetic Field Lines |
| title_short | Knot Probability of Random Magnetic Field Lines |
| title_sort | knot probability of random magnetic field lines |
| topic | knot solar physics magnetic field |
| url | https://www.mdpi.com/2218-1997/11/4/110 |
| work_keys_str_mv | AT andaxiong knotprobabilityofrandommagneticfieldlines AT shangbinyang knotprobabilityofrandommagneticfieldlines AT xinliu knotprobabilityofrandommagneticfieldlines |