Piero Martin Consorzio RFX- Associazione Euratom-ENEA sulla fusione, Padova, Italy
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Transcript of Piero Martin Consorzio RFX- Associazione Euratom-ENEA sulla fusione, Padova, Italy
European Ph.D. course . - Garching 29.09.08) p.martin
Piero Martin
Consorzio RFX- Associazione Euratom-ENEA sulla fusione, Padova, ItalyDepartment of Physics, University of Padova
Notes for the lecture at the European Ph.D. Course (Garching, 28 September 2009)
Reversed Field Pinch:
equilibrium, stability and transport
European Ph.D. course . - Garching 29.09.08) p.martin
Note for users
These slides are intended only as tools to accompany the lecture. They are not supposed to be complete, since the
material presented on the blackboard is a fundamental part of the lecture.
European Ph.D. course . - Garching 29.09.08) p.martin
Outline of the lecture
1) MHD equilibrium basics
2) 1d examples
1) Q-pinch
2) Z-pinch
3) Screw pinch
3) RFP equilibrium basics
4) RFP Stability
5) RFP dynamics and the dynamo.
6) Effects on transport
European Ph.D. course . - Garching 29.09.08) p.martin
RFP exist: e.g. RFX-modRFP exist: e.g. RFX-mod
a=0.459 m, R=2 m, plasma current up to 2 MA
The largest RFP in the world, located in Padova, Italy
A fusion facility for MHD mode control
A dynamic and well-integrated community
RFX-modRFX-mod EXTRAP T2REXTRAP T2R RELAXRELAX MSTMST
StockholmStockholm
PadovaPadovaKyotoKyoto
MadisonMadison
Princeton Plasma Physics Laboratory Colloquium - June 4th, 20092008 IAEA Fusion Energy Conference, Geneva - P. Martin
The RFP: a tight link with University
(all experiments in University environment)
and a nursery for the fusion community
DOE Fusion Science, Germantown, MD - 23/07/2008 p.martin
Most of the RFP magnetic field is generated by current flowing in the plasma (driven also by a
dynamo mechanism)No need for large magnetic coils.
The distinctive feature of the RFP that motivates its interest as a fusion energy system is the weak applied toroidal magnetic field.
The RFP configuration is similar to a tokamak…
– like to the tokamak, the RFP is obtained by driving a toroidal electrical current in a plasma embedded in a toroidal magnetic field pinch effect.
…..but the applied toroidal field is 10 – 100 times weaker !
RFP: exploiting the weak field
DOE Fusion Science, Germantown, MD - 23/07/2008 p.martin
Why the RFP ?
A current-carrying low magnetic field configuration as the RFP:
– has several technological advantages as a potential reactor configuration and will therefore contribute to the development of a viable reactor concept
– has unique capabilities to contribute to fusion energy science and technology research
DOE Fusion Science, Germantown, MD - 23/07/2008 p.martin
Fusion potential of the low magnetic field
high engineering beta
– For configurations like the tokamak the maximum field at the magnet is of order twice the field in the plasma, whereas in the RFP the field at the magnet is less than in the plasma.
– The engineering beta in an RFP reactor might be as much as twice the physics beta (up to 26% in present experiments)..
Use of normal (rather than superconducting) coils,
High mass power density,
Efficient assembly and disassembly,
Possibly free choice of aspect ratio
coils) (at the pressure magnetic averaged-surface
pressure averaged-volume=β
DOE Fusion Science, Germantown, MD - 23/07/2008 p.martin
A comprehensive understanding of toroidal magnetic confinement, and the possibility of predicting it, implies that plasma behavior would be predictable over a wide range of magnetic field strengths.
The RFP provides new information since it extends our understanding to low field strength, testing the results derived at high field with the tokamak.
European Ph.D. course . - Garching 29.09.08) p.martin
The MHD equilibrium problem
Time-indpendent form of the full MHD equations with v=0
European Ph.D. course . - Garching 29.09.08) p.martin
Current, magnetic and pressure surfaces
The angle between J and B is in general arbitrary
European Ph.D. course . - Garching 29.09.08) p.martin
Revisiting stochastic magnetic fields in present day fusion devices
Coils like these are presently under consideration in ITER to produce, by purpose, stochastic magnetic field for ELM suppression (Resonant Magnetic Perturbation)
European Ph.D. course . - Garching 29.09.08) p.martin
One-dimensional configurations
Even if the magnetic configurations of fusion interest are toroidal, some physical intuition can be obtained by investigating their one-dimensional, cylindrically simmetric versions.
This separates:
– Radial pressure balance
– Toroidal force balance
For most configurations, once radial pressure balance is established, toroidicity can be introduced by means of an aspect ratio expansion, from which one can then investigate toroidal force balance.
European Ph.D. course . - Garching 29.09.08) p.martin
A simple example: -pinch
Configuration with pure toroidal field
European Ph.D. course . - Garching 29.09.08) p.martin
A simple example: -pinch
The sum of magnetic and kinetic pressure is constant throughout the plasma
The plasma is confined by the pressure of the applied magnetic field
European Ph.D. course . - Garching 29.09.08) p.martin
Experimental -pinch
Experimental -pinch devices among the first experiments to be realized
End-losses severe problem
A -pinch is neutrally stable, and can not be bent into a toroidal equilbrium
Additional field must be added to provide equilibrium
European Ph.D. course . - Garching 29.09.08) p.martin
Z-pinch
Purely poloidal field
All quantities are only functions of r
European Ph.D. course . - Garching 29.09.08) p.martin
Z-pinch
In contrast to the -pinch, for a Z-pinch it is the tension force and not the magnetic pressure gradient that provides radial confinement of the plasma
The Bennet pinch satisfies the Z-pinch equilibrium
European Ph.D. course . - Garching 29.09.08) p.martin
Bennet Z-pinch
Tension force acts inwards, providing radial pressure balance.
European Ph.D. course . - Garching 29.09.08) p.martin
Z-machine
The Z machine fires a very powerful electrical discharge (several tens million-ampere for less than 100 nanoseconds) into an array of thin, parallel tungsten wires called a liner.
Originally designed to supply 50 terawatts of power in one fast pulse, technological advances resulted in an increased output of 290 terawatts
Z releases 80 times the world's electrical power output for about seventy nanoseconds; however, only a moderate amount of energy is consumed in each test (roughly twelve megajoules) - the efficiency from wall current to X-ray output is about 15%
At the end of 2005, the Z machine produced plasmas with announced temperatures in excess of 2 billion kelvin (2 GK, 2×109 K), even reaching a peak at 3.7 billion K.