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Plasma Diamagnetism and Solar Coronal Activity

Plasma Diamagnetism and Solar Coronal Activity. Kiyoto Shibasaki Nobeyama Solar Radio Observatory. Outline. Observational evidences (loop top plasma concentration) Existing model Propose a new model based on plasma diamagnetism ( NOT heating mechanism BUT confinement mechanism )

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Plasma Diamagnetism and Solar Coronal Activity

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  1. Plasma Diamagnetism and Solar Coronal Activity Kiyoto Shibasaki Nobeyama Solar Radio Observatory SBSM6@Kyoto

  2. Outline • Observational evidences (loop top plasma concentration) • Existing model • Propose a new model based on plasma diamagnetism (NOT heating mechanism BUT confinement mechanism) • Application of diamagnetic force to other phenomena • Summary and discussion

  3. 1. Soft X-ray Observations of loop top plasma concentration • Observations by Yohkoh/SXT • Feldman Blob (Acton ’92, Feldman ’94, etc.)

  4. Summary of physical parameters of loop-top concentration • Temperature：１～２×１０７K • Density：１０１１～１０１２ｃｍ－３ • Temperature distribution： • Temperature decreases from the top toward legs • Appearance phase： • Flare main phase ~ post-flare phase

  5. 2. Existing model Jakimiec, J., Tomczak, M., Falewicz, R., Phillips, K. J. H., and Fludra, A., A&A 334, 1112-1122 (1998).

  6. 3. A new model based on plasma diamagnetism • Larmor radius and mean free path • Electron Larmor radius：Lp ~ 103 T6/BG cm • Proton Larmor radius：Le ~ 20 T6/BG cm • Mean free path of electrons and protons：λ~ 107 T62/N9 cm • N9~103, T6~10, BG~100： Lp, Le << λ Lp~100 cm, Le~2cm, λ~106 cm Plasma is strongly magnetized • Gyration of charged particles: current ring ⇒ magnet • Magnetic moment （both for electrons and protons）　 μ＝ｍｖ⊥2／(2B) = kT/B、　M = 2Nμ= 2N kT/B

  7. Confinement Mechanism (Dia-)magnet in magnetic field with gradient is pushed toward weaker field region. Diamagnetic force μ(dB/dr) (or mirror force) Magnetic field (B) magnetic moment（μ）

  8. Force Balance Assuming high-pressure region is located at the top left ：upward force（diamagnetic force） right：downward force（gravity＋pressure gradient） 2NkT/B dB/dr = Nmpg0 + dP/dr; P = 2NkT 1/ｌB = 1/H0 + 1/ｌｐ ｌｐ= P/(dP/dr), ｌＢ=B/(dB/dr), H0=2kT/mpg0 Condition for high pressure area at the loop top（ｌｐ>0 ）: ｌB (curvature radius～loop height) < H0（~ 6×109T6 cm）

  9. Plasma as magnetized media • B = H + 4πM • M = - 2NkT/B (B/B) • Magnetic energy（in case of non-linear media）: δU = (1/4π) H・δB= (B/4π - M)・δB = δ(B2/8π) + 2NkT/BδB • Magnetic force: F = - dU/ds = - d/ds (B2/8π) - 2NkT/B dB/ds 　　　　　　 melon seed force diamagnetic force • Particle view and media view agreed. • Diamagnetic force does not depend on absolute value of B • Melon seed force exists without plasma

  10. FJ dS S dx x • Fig. Small segment of a loop filled with plasma （ x ~ x+dx) • Magnetic field strength decreases toward x-direction. • FJ=JxB(=P) force is applied perpendicular to the magnetic line of force surrounding the loop MHD treatment • FJ is applied on the edge strip of the truncated cone. The x-component of the total applied force is: FJdS = PdS. • The volume of the truncated cone is Sdx. Hence the force per volume is f = P/S dS/dx • Due to magnetic flux conservation (BS=const.), dS=-S/B dB • As the result, f＝ - P/B dB/dx (agree with particle treatment)

  11. 4.Plasma flow along open magnetic field • F = 2NkT/ｌB = 4NkT/r 　　　(Solar wind driving term by Parker) • radial magnetic field: ｌB = r/2 (r: distance from the solar center) • Steeper than ｒ-2results in stronger acceleration (such as in polar coronal holes) • Ｖ⊥≫Ｖ||　(UVCS obs.) results in strong acceleration • In closed magnetic loops with large asymmetry • Flows with acceleration is expected • Plasmoid Ejection :Ohyama M. & Shibata K. 1998, ApJ, 499, 934 (associated with a flare) • Jets：Shimojo, M., Hashimoto, S., & Shibata, K. 1996, PASJ, 48, 123 (associated with micro flares)

  12. Others • High-beta region is spontaneously created at the loop top where magnetic curvature is smaller. • Ballooning instability (or high-beta disruption) is expected (localized interchange instability) • Foot points of hot loops are diffuse (SXT) due to less density (or EM) at foot points.

  13. 5. Summary and Discussion • Hot-and-dense plasma confinement is due to diamagnetic force of plasma along magnetic loop • This force can be explained by particle treatment, treatment as magnentized media and also MHD treatment. • In general, magnetic field becomes weaker outwards, hence we expect various ejections against strong gravity. Diamagnetism of plasma can be the origin of solar activity in hot corona. Energy should be supplied by unknown heating mechanism.

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