2005 Plasma Diamagnetism and Solar Coronal Activity Kiyoto Shibasaki Nobeyama Solar Radio Observatory

Outline 1.Observational evidences (loop top plasma concentration) 2.Existing model 3.Propose a new model based on plasma diamagnetism (NOT heating mechanism BUT confinement mechanism) 4.Application of diamagnetic force to other phenomena 5.Summary and discussion

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

Summary of physical parameters of loop-top concentration Temperature ：１～２ × １０ ７ K Density ：１０ １１ ～１０ １２ ｃｍ －３ Temperature distribution ： –Temperature decreases from the top toward legs Appearance phase ： –Flare main phase ~ post-flare phase

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

3. A new model based on plasma diamagnetism Larmor radius and mean free path –Electron Larmor radius ： L p ~ 10 3 T 6 /B G cm –Proton Larmor radius ： L e ~ 20 T 6 /B G cm –Mean free path of electrons and protons ： λ~ 10 7 T 6 2 /N 9 cm –N 9 ~10 3, T 6 ~10, B G ~100 ： L p, L e << λ L p ~100 cm, L e ~2cm, λ~10 6 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

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

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 = Nm p g 0 + dP/dr ; P = 2NkT 1/ ｌ B = 1/H 0 + 1/ ｌ ｐ ｌ ｐ = P/(dP/dr), ｌ Ｂ =B/(dB/dr), H 0 =2kT/m p g 0 Condition for high pressure area at the loop top （ｌ ｐ >0 ） : ｌ B (curvature radius ～ loop height) < H 0 （ ~ 6×10 9 T 6 cm ）

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(B 2 /8π) + 2NkT/BδB Magnetic force: F = - dU/ds = - d/ds (B 2 /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

MHD treatment S dx dS FJFJ x Fig. Small segment of a loop filled with plasma （ x ~ x+dx) Magnetic field strength decreases toward x-direction. F J =JxB(=P) force is applied perpendicular to the magnetic line of force surrounding the loop F J is applied on the edge strip of the truncated cone. The x- component of the total applied force is: F J dS = 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)

4.Plasma flow along open magnetic field F = 2NkT/ ｌ B = 4NkT/r (Solar wind driving term by Parker) – radial magnetic field: ｌ B = r/2 (r: distance from the solar center) –Steeper than ｒ -2 results 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)

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.

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.