mhd limit cycles on ftustatic.sif.it/.../public/files/congr16/mc/casolari.pdf · 2017. 1. 10. ·...

Andrea Casolari - Università di Pisa 1

MHD limit cycles on FTU

Andrea Casolari*†

Paolo Buratti**, Gianluca Pucella**, Edmondo

Giovannozzi** & Daniela Grasso‡

*Dipartimento di Fisica Enrico Fermi, Università di Pisa, Pisa, Italy †ENEA guest

**ENEA-FSN-FUSPHY-TSM, C. R. Frascati, Frascati, Italy‡ISC-CNR and Politecnico di Torino, Torino, Italy


Outline of this work

A new regime of propagation of magnetic islands has been observed in FTU

In this regime, islands show a periodic modulation of amplitude and rotation frequency

The time scale characterizing the amplitude growth is much smaller than the resistive time

From the analysis of experimental data we deduced the presence of harmonics island deformation

Numerical simulations show the deformation of the island due to diamagnetic effects


Magnetic islands

● Equilibrium magnetic flux surfaces

● Plasma equilibrium is affected by instabilities

● Tearing mode magnetic islands


Normal regime vs limit cycles


Limit cycles on FTU

The trajectory of a point describing the state of the system is a cycle

G.Pucella, P.Buratti, C.Cianfarani, E.Giovannozzi and FTU team, 42th EPS conference on plasma physics, 2015


MHD thresholds


Harmonics

The period of one cycle is about 3 ms, while the resistive time is about 260 ms


Fluid equations

The two-fluid system of equations can be reduced to a modified version of the four-field model, originally deduced by Hazeltine, Kotschenreuter & Morrison

R.D. Hazeltine, M. Kotschenreuter & P.J. Morrison, Physics of Fluids 28.8 2466 (1985)

E+ve∧B+

1

en∇ P

e=η J

( ∂∂ t +vi⋅∇)n+n ∇⋅vi=0m

in( ∂∂ t +vi⋅∇)vi=J ∧B�∇ P�∇⋅πi+µ∇ 2 vi


Numerical integration

A 2D slab finite-difference code can be used to integrate the time-dependent four-field equations

The code uses periodic boundary conditions in y and by imposing that the fields go to zero at large x

We choose the Harris current sheet as magnetic equilibrium

We impose an equilibrium density gradient, providing a drift velocity to the plasma

D. Grasso, D. Borgogno & E. Tassi, Communications in Nonlinear Science and

Numerical Simulation 17 2085 (2012)

B=B0 tanh (x / Ls)

n=n0(1+ x /Ln)


Island deformation

The simulations show the island deformation in the direction of motion, caused by the diamagnetic effects

The island deformation occurs only with large drift velocities


Island deformation

By changing the parameters of the simulation it is possible to emphasize the island deformation

From the previous simulation, the drift frequency was doubled


Density flattening

As the island grows nonlinearly, the density becomes a flux function and the density profile becomes flat inside the separatrix


Conclusions

● Limit cycles are periodic variation of frequency and amplitude of magnetic islands

● The limit cycles only occur in the high density discharges

● The Fourier analysis of the experimental signal shows the presence of harmonics island deformation

● The numerical simulations show a deformation of the island

● The deformation occurs when the islands are large enough to flatten the density profile inside the separatrix


Future prospectives

The island deformation accounts for the harmonic content of the signals

The role of the harmonics on the cyclic evolution of amplitude and frequency need further investigation

The time scale of the island growth is much smaller than the resistive time

A fundamental understanding of this regime is still missing


Thanks for the attention

mhd limit cycles on ftustatic.sif.it/.../public/files/congr16/mc/casolari.pdf · 2017. 1. 10. ·...

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