Projekttitel

• The impact of stochastic magnetic fields on rotation and the radial electric field in the edge of tokamak plasmas


• Experimental studies on open helical ergodic divertors


• Numerical methods for eigenvalue problems in the description of drift instabilities in the plasma edge


• Laser-driven hard x-ray source


• Inverse bremsstrahlung in a strong laser field


• Strong field laser interaction with matter


• 3D plasma flow simulations in ergodized magnetic fields


• Characterization of ergodic magnetic fields by means of injection of fast frozen hydrogen pellets


• Investigation of electron transport in the plasma boundary of a tokamak


• Investigation of the influence of ergodic field structures on impurity transport in magnetically confined high temperature plasmas


• Models for fluctuation-induced transport and generation of transport barriers


• Nonlinear dynamics of laser driven and dissipative systems far from equilibrium


• Edge localised modes and their effect on global plasmas behaviour


• Production of hot, dense plasmas using sub-ten femtosecond laser pulses


• Interaction of intense radiation and particle sources with walls


• Resonant MHD coupling of external helical magnetic field perturbations in tokamak plasmas

The impact of stochastic magnetic fields on rotation and the radial electric field in the edge of tokamak plasmas

Radial electric field, plasma rotation and shear of those quantities have significant impact on turbulence and transport in the edge of tokamak plasmas, in particular with respect to the formation of transport barriers (as typical for so-called High Confinement Mode (H-mode- ) plasmas) and the power threshold to access such H-mode conditions [1]. It is known from previous tokamak experiments, that resonant magnetic perturbations and the formation of stochastic magnetic fields at the plasma boundary strongly influence electric field and rotation [2] [3]: In the perturbed region a positive electric field develops – that should counter- act the formation a negative well of the radial electric field, which is typical for the H-mode, and must be a concern.

On the other hand, the application of resonant magnetic perturbations has allowed to control the edge pressure profiles in H-mode discharges and to avoid excessive transient heat loads which are associated with edge instabilities driven by the enhanced pressure gradients under H-mode conditions (so called edge localised modes – ELMs) [4]. Therefore, the physical mechanisms, which determine the radial electric field and the plasma rotation in stochastic magnetic fields, must be understood to assess the feasibility of such ELM suppression schemes for future fusion devices.

Within this project, we plan to investigate the role of the radial electric field and the plasma rotation with upgraded diagnostics to measure the radial profile of poloidal and toroidal plasma diagnostics as well as the radial electric field using active charge exchange diagnostics with a hydrogen diagnostics beam [5]. Complementary diagnostics are at hand to compare with the spectroscopic results: a fast reciprocating probe system allowing the measurement of potential profiles across the perturbed plasma edge and a reflectometer system to deduce the rotation of turbulent structures.

The aim of the project is to identify the physical mechanism of torque transfer in stochastic magnetic fields, which gives rise to plasma rotation and governs the changes of the radial electric field. One possible mechanism relies on the onset of transverse currents in the ergodic region [6]. Another possibility is connected to the onset of shielding currents developing at rational surfaces [7].

The scope of this project comprises experiments at the tokamak TEXTOR using the Dynamic Ergodic Divertor (DED) [8] in both static and dynamic operation with rotation frequencies of the magnetic perturbations up to 10 kHz. The flexibility of the DED to operate in different base mode configurations (m/n= 3/1, 6/2 or 12/4) shall be used to vary the width and structure of the perturbed plasma volume.

References
[1] K.H. Burrell, Phys. Plasmas 4, 1499 (1997)
[2] X.Z. Yang et al., Physics of Fluids B: Plasma Physics 3 (1991), Nr. 12, 3448.
[3] W.R. Hess et al., Plasma Physics and Controlled Fusion 37 (1995), Nr. 9, 951 and Ph. Ghendrih et al., Plasma Physics Controlled Fusion 38 (1996) 1653-1724
[4] T.E. Evans et al., Physical Review Letters 92 (2004), Nr. 23, 235003.
[5] A.A. Ivanov, V.I. Davydenko, P.P. Deichuli, A. Kreter, V.V. Mishagin, A.A. Podminogin, I.V. Shikhovtsev, B. Schweer and R. Uhlemann, Radio frequency ion source for plasma diagnostics in magnetic fusion experiments, Review of Scientific Instruments 71, 3728 (2000)
[6] I. Kagonovich and V. Rozhansky, Physics of Plasmas 5 (1998), Nr. 11, 390.
[7] Y. Kikuchi et al., Contrib. Plasma Phys. 46, No. 7-9, 539-544 (2006).
[8] K.H. Finken (Ed.), Special Issue: Dynamic Ergodic Divertor, Fusion Engineering and Design 37 (1997) 335.

Experimental studies on open helical ergodic divertors

The exhaust of power and particles from magnetically confined fusion plasmas is a key issue on the way to a future reactor. A promising concept to control power and particle exhaust is the divertor which provides a controlled interaction zone between plasma and wall components. While much experience and physical understanding has been gained in poloidal divertor tokamaks [1], the physical mechanisms governing divertor configurations in confinement devices with inherent 3-D structures as stellarators and other helical devices (cf. [2] and references therein) are much less understood because of the more complex geometry.

Divertor structures similar to those in helical devices can also be obtained in tokamaks by means of external perturbation coils [3] [4], which give rise to a stochastic magnetic field in the plasma edge layer comprising both an ergodic zone and an open helical ergodic divertor structure in the near- field of the perturbation coils. Along with the similarity of the topology of the magnetic field in helical devices and tokamaks with external perturbation coils, common physical mechanisms can be expected at work as e.g. momentum losses along the flow channels of the plasma towards the plasma facing components caused by ion friction.

In recent years a numerical code has become available to model plasma transport in those 3-dimensional geometries (the 3-dimensional Monte Carlo code EMC3 – Eirene, cf. [5] and references therein). However, also experimental studies are needed to benchmark such models for application to future helical devices as the stellarator Wendelstein 7-X which is presently constructed in Greifswald, Germany.

The aim of this project is to characterize experimentally helical divertor structure of the Dynamic Ergodic Divertor [6] in the tokamak TEXTOR. Here the topology of the divertor can be flexibly varied by changing the mode spectrum of the magnetic perturbation with base mode numbers m/n = 3/1, 6/2 and 12/4. This work comprises the determination of local plasma parameters in the divertor region as density and temperature, the plasma flow characteristics, the particle flux distribution onto the divertor target as plasma facing component, the recycling flux characteristics and the source distribution stemming from ionization processes in front of the wall. From such measurements, screening properties of the divertor shall be derived and related to global plasma behavior.

The base technique to be applied is optical spectroscopy of neutral atoms and molecules (fuel and impurity neutrals) [7] [8]. Such techniques have been proven successful to determine both the characteristics of the recycling processes on plasma facing components [9] and local plasma parameters [7][10]. Additional diagnostics as Langmuir probes and IR thermography are available to complement the measurements in the ergodic divertor region.

References
[1] P.C. Stangeby, The Plasma Boundary of Magnetic Fusion Devices, Plasma Physics Series, IoP Publishing Ltd, Bristol, UK (2000)
[2] R König et al., Plasma Phys. Control. Fusion 44 (2002) 2365-2422.
[3] Ph. Ghendrih et al., Plasma Physics Controlled Fusion 38 (1996) 1653-1724
[4] M. Lehnen et al., Plasma Physics and Controlled Fusion 47 (2005), B237.
[5] M. Kobayashi et al., Nucl. Fusion 44 No. 6 (2004), 74.
[6] K.H. Finken (Ed.), Special Issue: Dynamic Ergodic Divertor, Fusion Engineering and Design 37 (1997) 335.
[7] U. Fantz, Plasma Sources Sci. Technol. 15 No 4 (November 2006) S137-S147, and U. Fantz, Atomic and molecular emission spectroscopy in low temperature plasmas containing hydrogen and deuterium, IPP Report, IPP 10/21
[8] A. Pospieszczyk, Diagnostics of edge plasmas by optical methods, Atomic and Plasma- Material Interaction Processes in Controlled Thermonuclear Fusion, ed. R.K. Janev and H.W. Drawin (Amsterdam : Elsevier) (1993)
[9] S. Brezinsek et al., Plasma Phys. Control. Fusion 47 No 4 (April 2005) 615-634 [10] B. Unterberg et al., Journal of Nuclear Materials 337-339 (2005) (1-3 SPEC. ISS.): 515-519.

Numerical methods for eigenvalue problems in the description of drift instabilities in the plasma edge

The aim of this project is to develop efficient numerical methods for the solution of dispersion equations, which play a role in the treatment of drift instabilities in hot, strongly inhomogeneous plasma. These instabilities determine the so-called anomalous transport of particles and the energy in fusion devices.

The starting point of our work is a nonlinear variant of the Mathieu equation where the 2π periodic solution of interest is that for which the imaginary part of the frequency is maximal. The numerical problem is closely related to an eigenvalue PDE problem. A standard approach for solving these type of problems is to use a discretization scheme in the spatial direction and subsequently solve the algebraic eigenvalue problem, see, e.g., [1]. The problem here differs in the sense that after spatial discretization a nonlinear eigenvalue problem results. Initial research has indicated that the problem can be formulated as a quadratic eigenvalue problem.

The numerical solution of quadratic eigenvalue problems has recently attracted a lot of attention in the numerical linear algebra community and signifficant steps have been taken towards the understanding and solution of this type of problem, see [2]. A standard solution technique in this context is to reformulate the problem as a generalized eigenvalue problem and solve this problem using standard methods. However, there are research efforts that learn that for sufficiently accurate approximations special care might be necessary to exploit the structure of the underlying problem [3]. Alternatively, when only a few eigenvectors are required or the matrix is large and sparse, shift and invert techniques [4] or Jacobi-Davidson methods are most effective [5]. The efficiency and accuracy of the algorithm plays an important role in the current context since the solutions of the eigenproblem should be used in the self-consistent description of the influence of instabilities on the transport processes in the plasma.

In the second part of the project, we plan to investigate numerically solving variants of the above mentioned equation where the frequency depends on the angle coordinate. Such dependence reflects the strong inhomogeneity of the plasma parameter that, for example, occurs close to the density limits. This problem is a nonlinear eigenvalue problem that cannot be transformed to a problem of polynomial type and requires a full nonlinear solver. Related problems are for example studied in [6].

The research plan for this project is as follows: First we intend to investigate the discretization of the problem and the effect on the error of the required approximations. This includes the choice of appropriate boundary conditions. Subsequently we investigate the solution of the polynomial eigenvalue problem. Initial numerical experiments for the present problem have shown that straightforward linearization techniques can result in a spectrum for which some eigenvalues are very sensitive towards perturbation. We will study this behavior in detail and derive error bounds on the quality of the computed approximations. In the second part of the project, we plan to study the full nonlinear problem.

References
[1] Zhaojun Bai, James Demmel, Jack Dongarra, and Axel Ruhe (eds.), Templates for the solution of algebraic eigenvalue problems, Software, Environments, and Tools, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2000, A practical guide.

[2] Françoise Tisseur and Karl Meerbergen, The quadratic eigenvalue problem, SIAM Rev. 43, 235 (2001) (electronic)

[3] Volker Mehrmann and David Watkins, Polynomial eigenvalue problems with Hamiltonian structure, Electron. Trans. Numer. Anal. 13, 106 (2002) (electronic)

[4] Karl Meerbergen, Locking and restarting quadratic eigenvalue solvers, SIAM J. Sci. Comput. 22, 1814 (2000) (electronic).

[5] Gerard L. G. Sleijpen, Albert G. L. Booten, Diederik R. Fokkema, and Henk A. Van der Vorst, Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems, BIT 36, 595 (1996), International Linear Algebra Year (Toulouse, 1995)

[6] Axel Ruhe, Algorithms for the nonlinear eigenvalue problem, SIAM J. Numer. Anal. 10, 674 (1973)

Laser-driven hard x-ray source

Laser-produced plasmas are well-suited to generate of x-ray radiation. In the last couple of years, many groups have worked on sources of ultrashort pulses of keV radiation (2-10 keV), and they have obtained enough photon flux to apply these x-rays to first experiments, for example on the dynamics of structural changes at surfaces. Our group is also involved in this research with a project in the DFG-funded priority program 1134 Strukturanalyse mit Ultrakurzzeit-Röntgenmethoden. In the project proposed here, the intention is to increase the photon energy of such sources to the multi-ten-keV range (20-150 keV). Such x-rays are typically used in medicine. In the long term, ultra-short x-ray pulses in this energy range may lead to a substantial decrease of the patients' radiation dose when only ballistic photons are detected and all the scattered radiation is blocked by a fast switch. These ideas have been around for about ten years, and proof-of-principle ex- periments have been conducted (e.g. [1]), but there has not been much progress since then.

For producing hard x-rays of energy hν in dense matter, electrons of energy kT are required which should be typically kT ≈ 3hν. When these electrons are generated at solid surfaces by classical laser-matter interaction, one ends up with an optimum laser intensity for a certain wanted x-ray energy, for example of I_opt ≈ 2⋅10¹⁸ W/cm² for Ta-Kα (57 keV) [2]. In the last couple of years it was shown that high-intensity interaction is favourable for hard x-ray creation since highly directed beams of electrons can be created which produce harder and more intense x-rays than assumed by the scaling mentioned above. Ultra-intense 8-keV x-ray pulses of much reduced source size and a supposed ultra-short duration were created in this regime [3].

In the project proposed, the focus is on extending this research into the hard x-ray regime using ultrashort pulses of only a few cycles duration with powers exceeding 1 TW. Compared to lasers with longer pulses as used in all the previous work, the interaction with the new Düsseldorf laser will be strongly modified. The light-to-x-ray conversion is expected to be enhanced because classical collective energy transfer processes (like resonance absorption) lose importance compared to direct field interaction processes. Therefore, this new interaction regime must be investigated and optimized with regard to the x-ray production - an ideal situation for a high-level PhD project.

All the required specialized know-how and diagnostics are available, like an imaging plate diagnostics system, a sub-ps x-ray streak camera, crystals for x-ray spectroscopy, methods for obtaining spatial resolution, electron spectrometers etc. Other projects on laser-matter interaction, particle acceleration and (softer) x-ray generation within this Research Training Group, in the Transregio SFB/TR18 and at the Institute of Laser- and Plasma Physics will create a productive atmosphere and ideal conditions for this project.

References
[1] C.L. Gordon III, G.Y. Yin, B.E. Lemoff, P.B. Bell, C.P.J. Barty, Time-gated imaging with an ultrashort pulse, laser-produced-plasma x-ray source, Opt. Lett. 20, 1056 (1995);
M. Grätz, A. Pifferi, C.G. Wahlström, S. Svanberg, Time-gated imaging in radiology: theoretical and experimental studies, IEEE J. Sel. Top. Quantum Electron. 2, 1041 (1996)

[2] G. Pretzler, T. Schlegel, E. Fill, D. Eder, Hot electron generation in copper and photopumping of cobalt, Phys. Rev. E 62, 5618 (2000);
C. Reich, P. Gibbon, I. Uschmann, E. Förster, Yield optimization and time structure of femtosecond laser plasma Kα sources, Phys. Rev. Lett. 84, 4846 (2000)

[3] G. Pretzler, F. Brandl, J. Stein, E. Fill, J. Kuba, High-intensity regime of x-ray generation from relativistic laser plasmas, Appl. Phys. Lett. 82, 3623 (2003);
F. Brandl, G. Pretzler, D. Habs, E. Fill, Cerenkov radiation diagnostics of hot electrons generated by fs-laser interaction with solid targets, Europhys. Lett. 61, 632 (2003)

Inverse bremsstrahlung in a strong laser field

In low-intensity laser matter interaction, inverse bremsstrahlung is the dominant absorption mechanism under certain conditions. The effect has been thoroughly investigated in the last decades and is well understood. In the classical approach, the efficiency of the process decreases with increasing intensity. In the last couple of years, several theoretical groups have worked on binary collisions in strong laser fields and have shown that nonlinear processes as correlated electron collisions or Coulomb focusing lead to strongly enhanced electron energy gain and inverse bremsstrahlung heating rates. Simulations predict further that together with this enhancement, the standard isotropic and Maxwellian electron distribution function is modified and significant non-thermal portions of the spectrum develop as well as preferred electron directions [1].

In this project, the absorption of ultrashort and strong laser pulses will be studied experimentally in preformed elongated plasma, with special emphasis on the electron-ion collisions and their effect on absorption. This will be done with the new Düsseldorf high-intensity laser, but since the highest intensities are not needed at the beginning, there will be the chance to vary not only the pre-plasma conditions and pulse energy, but also pulse duration effects in the range of 10 fs up to ∼ 10 ps - a unique possibility which is expected to show the transition between essentially collision-free single-particle effects and the collision-dominated inverse bremsstrahlung regime.

Since the primary effects (i.e. details of the electron energy distributions) are not acces- sible, proper indirect diagnostics is the key for experiments on this topic:

• The effect of the propagation through plasma on the laser pulse will be studied under different conditions. Detailed phase-sensitive diagnostics (like with a SPIDER-device) yields much more than just the overall absorption, but also information on ionisation rates (by the blue-shift) or induced non-linearities (by the spectral/temporal pulse shape).


• Coherently scattered light to distinct directions is a footprint of the electron populations during interaction.


• Spectroscopy from the VUV to the x-ray range allows conclusions on the electron temperatures. When done with spatial resolution and under different laser polarization directions, it can also be a measure for inhomogeneities.


• The temperature and its spatial distribution are also revealed by plasma expansion measurements.


• Escaping electrons can be detected by an electron TOF spectrometer; directional information is obtained by rotating the laser polarization direction.

The experiments will be done in close cooperation with theory at the Institute for Theoretical Physics but also in a continuation of a present cooperation with Prof. R. Sydora (University of Edmonton, Canada) who is an expert on this field in theory. The project is ideally suited for a 3 year PhD project.

References
[1] A. Brantov, W. Rozmus, R. Sydora, C. E. Capjack, V. Y. Bychenkov, V. T. Tikhonchuk, Enhanced inverse bremsstrahlung heating rates in a strong laser field, Phys. Plasmas 10, 3385 (2003);
O. V. Batishchev, V. Y. Bychenkov, F. Detering, W. Rozmus, R. Sydora, C. E. Capjack, V. N. Novikov, Heat transport and electron distribution function in laser produced plasmas with hot spots, Phys. Plasmas 9, 2302 (2002);
H. J. Kull, V. T. Tikhonchuk, Fast electrons from electron-ion collisions in strong laser fields, submitted for publication (2004)

[2] G. Pretzler and E. Fill, Comparison of soft x-ray spectra from optical-field ionized plasmas generated with linearly and elliptically polarized fs-laser pulses, Phys. Rev. E 56, 2112 (1997);
E. Fill, G. Pretzler, R. Tommasini, B. Witzel, Analysis of the visible emission from optical-field ionized hydrogen, Europhys. Lett. 49, 27 (2000)

Strong field laser interaction with matter

Strong field laser interaction with matter leads to a number of new nonlinear effects [1]. Particularly important is the high harmonics generation. It is known that the atomic harmonics spectrum has a plateau with a sharp cut-off at the photon energy 3.2U_p + I_p, where U_p is the laser ponderomotive potential and I_p is the atomic ionization potential [2]. The high laser harmonics in the plateau region have correlated phases and emerge in the form of sub-femtosecond pulses [3]. Recently, it has been shown that the process of stimulated recombination [4] plays the central role in the harmonic production. It is a resonant process and it occurs when an electron wave packet extracted from the atoms re-encounters the incompletely ionized atom and interferes with itself still remaining in the ground state. The stimulated recombination leads to a highly efficient resonant emission at hν = Ekin + Ip in the form of attosecond pulses. The stimulated recombination strongly depends on the shape of the ground state electron Ψ-function. The up-to date theoretical studies have been limited to the spherically symmetric s-state of the active electron in a single atom.

In this project it is proposed to study the generation of high harmonics and attosecond pulses from laser interaction with solid surfaces at intensities close to the tunnelling ionization limit. The efficiency of the attosecond pulse production depends not only on the electron ground function, but also on the laser propagation effects in the medium. In this sense, harmonic generation via reflection from a solid surface can be energetically more efficient than the harmonic production in a gas medium, because the propagation effects on the surface are absent.

The project is ideally suited for a three-year PhD work. It includes development of a 3D numerical code for solution of Schrödinger equations. The laser-matter interaction will be treated within a single-electron model. The angular distribution of the generated X-rays gives a clue on the spatial distribution of the electron ground state function. Eventually, a „tomography“ of the electron state within material will be possible.

This work will be done in a close collaboration with Prof. F. Krausz group at Max- Planck-Institute for Quantum Optics, where a corresponding experiment is planned.

References
[1] A. Pukhov, Strong field interaction of laser radiation, Rep. Prog. Phys. 66, 47 (2003)

[2] M. Lewenstein, P. Balcou, M. Y. Ivanov, A. L'Huillier, P. B. Corkum, Theory of high harmonics generation by low frequency laser fields, Phys. Rev. A 49, 2117 (1994)

[3] A. Baltuska, T. Udem, M. Uiberacker, M. Hentschel, E. Goulielmakis, C. Gohle, R. Holzwarth, V. S. Yakovlev, A. Scrinzi, T. W. Hänsch, F. Krausz, Attosecond control of electronic processes by intense light fields, Nature 421, 611 (2003)

[4] A. Pukhov, S. Gordienko, T. Baeva, Temporal Structure of Attosecond Pulses from Intense Laser-Atom Interactions, Phys. Rev. Lett. 91, 173002 (2003)

3D plasma flow simulations in ergodized magnetic fields

Special external magnetic fields (Dynamic Ergodic Divertor / DED) are employed in the TEXTOR Tokamak (IPP, FZ-Juelich) to break the toroidal symmetry of the (fully magnetised) plasmas. This allows to produce plasmas of partial or fully developed magnetic field ergodizity, and to study plasma surface interaction in such magnetic field topologies. Conventional plasma fluid codes used to evaluate the plasma fields (temperature, density, flow fields) are not applicable, due to geometric and physical complexity. Monte Carlo methods for solving the partial differential fluid equations seem to remain the only option for a numerical quantification of contributing processes. In collaboration with the Max Planck Institute for Plasmaphysics, Greifswald (there: planned application to the W7X stellarator) and the National Institute of Fusion Science in Japan (there: planned appli- cations to the stellarator LHD) a 3-dimensional Monte Carlo code (EMC3-EIRENE) is developed, tested and applied.

Within the proposed project these concepts and methods shall be adapted and, if neces- sary, extended to achieve applicability as an interpretative tool for the experiments with the DED at TEXTOR. It shall furthermore be evaluated which plasma diagnostics need to be provided in order to fully constrain the computational model for achieving quan- titative results. In particular the (laminar) flow in the final part of quite thin magnetic flux tubes, which connect the ergodized plasma with the vessel and first wall structures, is to be studied in detail. Furthermore it shall be attempted to identify underlying simpler (reduced) models, perhaps with reduced dimensionality, which still contain the essential parts of the physics, if such simplified models exist.

For this firstly the numerical concept of "Greens-Function Monte Carlo" has to be studied and tested by operating the EMC3 code for specific applications. After this learning period detailed 3D simulations of plasma edge transport in TEXTOR-DED shall be carried out, in order to separate, computationally, classical and geometrical effects from the unknown turbulent (anomalous) cross field transport, and, by doing so, making the latter experimentally accessible. In the second year the theoretically open problem of the relative importance of the long, thin fluxtubes to the short but thicker fluxtubes, on heat and particle exhaust, shall be studied by numerical experiments. Furthermore, the so called "Divertor-Regime" (low-recycling, high-recycling, detachment) and transitions between them shall be studied, investigating whether at all ergodic divertor boundary layers can be classified by one or more of these three categories known from axis-symmetric poloidal divertors.

Similar efforts have been and are currently still undertaken, with the same computational model (EMC3-EIRENE) in Japan (LHD) and MPI Greifswald (there: data interpretation and model assessment using W7AS data). In particular the transition to so called detached divertor states directly from low recycling (linear) conditions and without intermediate high recycling regime have been found computationally, and later be confirmed experimentally with the island divertor in W7AS. As can also be seen from the list of published work (2001-2004) the proposed project is to be regarded as a long term study. One main future application will be the W7X stellarator (scheduled experimental start: 2010). In this regard the present studies on existing tokamaks (TEXTOR-DED) and stellarators (LHD-Japan) serve, in addition to their own scientific relevance, as model verification and assessment for this next gen- eration fusion device in Germany. Publication. previous work , Projekt EMC3, 2001-2004

References
[1] Runov, A., Reiter, D., Kasilov , S., et al. Monte Carlo Study of heat conductivity in the ergodic divertor of TEXTOR Physics of Plasmas, 8, No. 3, 916 (2001)

[2] Feng, Y., Sardei, F., Grigull P., McCormick K., Kisslinger, J., Reiter, D., Igitkhanov Y., Transport in island divertors: physics, 3D modelling and comparison to first experiments on W7-AS Plasma Physics and Controlled Fusion, 44, 5, 611 (2002)

[3] Kasilov S., Reiter, D., Runov A., Kernbichler W., Heyn M. On the magnetic nature of electron transport barriers in tokamaks Plasma Physics and Controlled Fusion, 44, 6, 985 (2002)

[4] Runov, A., Kasilov, S., Riemann, J, Borchardt, M., Reiter, D., Schneider, R., Benchmark of the 3-Dimensional plasma transport codes E3D and BoRiS Contrib. Plasma Physics 42, 169 (2002)

[5] Feng, Y., Sardei, F., Kisslinger, J., Reiter, D., Igithkanov, Y. Island Divertor Transport Modelling and Comparison with Experiment Contrib. Plasma Physics 42, 187 (2002)

[6] Feng, Y., Sardei, F., Grigull, P., McCormick, K., Giannone, L., Kisslinger, J., Reiter, D., Igitkhanov, Y., Wenzel, U. Modelling of island divertor physics and comparison to W7-AS experimental results J. of Nucl. Mater. 2003, 313-316, 857 (2003),

[7] Runov A., Kasilov S., Reiter D., McTaggert N., Bonnin X., Schneider R. Transport in Complex Magnetic Geometries: 3-Dimensional Modelling of Ergodic Edge Plasmas in Fusion Experiments J. of Nucl. Mater. 2003, 313-316, 1292 (2003),

[8] Feng, Y., Sardei, F., Kisslinger, J., Grigull, P., McCormick, K., Reiter, D. 3D Edge Modelling and Island Divertor Physics (9th internat. Workshop on Plasma Edge Theory in Fusion Devices, San Diego, Sept.2003) Contrib. Plasma Physics, 44, 1-3, 57 (2004)

[9] Runov, S.V. Kasilov, N. McTaggart, R. Schneider, X. Bonnin, R. Zagrski and D. Reiter Transport modelling for ergodic configurations Nucl. Fusion 44 No 6, 74 (June 2004)

[10] M. Kobayashi, Y. Feng, F. Sardei, D. Reiter, K.H. Finken and D. Reiser 3D numerical transport study of the edge ergodized plasma in TEXTOR-DED Nucl. Fusion 44 No 6, 64 (June 2004)

Characterization of ergodic magnetic fields by means of injection of fast frozen hydrogen pellets

In fusion research the injection of fast frozen hydrogen pellets serves the fuelling of the discharge with the necessary amount of hydrogen isotopes, the modification of the confinement properties of the magnetized plasma, the control of edge instabilities or the mapping of magnetic field lines in order to measure their orientation.
In the tokamak experiment TEXTOR in Jülich the hydrogen isotope is precipitated in a cryostat in tubes of 1.5 mm or 2.5 mm diameter. After the fast opening of a valve the frozen hydrogen pellet is accelerated to velocities of about 1 km/s. In subsequent steps the perturbing driver gas is separated from the pellet. The mass of the pellet is measured in a micro wave resonator. Finally the fast pellet enters the plasma discharge [1].
In contrast to the conventional method to generate a discharge by gentle gas puffing, the pellet penetrates deeply into the plasma. In doing so the pellet is heated by the energetic electrons of the plasma, resulting in the evaporation of the pellet ice. In this evaporation process a protecting gas cloud is formed around the pellet, which - similar to the Leidenfrost phenomena - reduces the ablation significantly.
For the work proposed here, the mapping of characteristic magnetic field structures by the pellet ablation is of particular interest. Recently a new experiment on TEXTOR went into operation: Helical magnetic field coils at the plasma boundary are used to produce resonant magnetic field perturbations in the plasma, which influence transport and stability of the plasma considerably. The unique property of this Dynamic Ergodic Divertor [2] is the possibility to rotate the magnetic field perturbation with frequencies of up to 10 kHz. Complementary to the SFB 591, here the specific emphasis is on the investigation of the ergodic magnetic field topology inside the plasma [3] and the resulting transport properties perpendicular and parallel to the perturbed magnetic field lines. Within the scope of this work the influence of the perturbed magnetic field topology shall be investigated. Utilizing a fast imaging camera (exposure time < 10 s) the pellet and ablating plasma can be traced along the magnetic field lines. The aim is to use this information to gain information on the characteristic properties of the ergodic magnetic field regions, the plasma confinement in magnetic islands and the transport perpendicular and parallel to such magnetic field structures.
Supplementary, the results of these studies could be compared with the 3-dimensional plasma flow simulations of the Dynamic Ergodic Divertor (see corresponding topic: 3D plasma flow simulations in ergodized magnetic fields). Furthermore, also the comparison with turbulence simulations of the perpendicular transport in the presence of helical magnetic field perturbations [4], which are part of a collaboration between the Max-Planck-Institut für Plasmaphysik and FZJ, could be envisaged.

References
[1] K. H. Finken, K. N. Sato, H. Akiyama, Plasma Phys. Control. Fusion 39 (1997) 351 [2] K. H. Finken (Guest Editor), Special Issue: Dynamic Ergodic Divertor, Fusion Engineering and Design 37, 337 (1997)

[3] M. C. Jakubowski, S. S. Abdullaev, K. H. Finken et al., Nucl. Fusion 44, 395 (2004)

[4] D. Reiser, B. Scott, Electromagnetic fluid drift turbulence in static ergodic magnetic fields, submitted to Phys. Plasmas (2004)

Investigation of electron transport in the plasma boundary of a tokamak

For the investigation of electron transport special emphasis should be put on complex magnetic field structures as can be generated with the Dynamic Ergodic Divertor (DED) on TEXTOR [1]. The DED ergodises locally particular regions of the edge plasma and generates magnetic islands in other regions via static or rotating (up to 10 kHz) distortion fields. Up to now there is a lack of knowledge about the energy and particle transport in such mixed systems (ergodic, islands, undistorted) [2]. For improved understanding a detailed determination of electron density and temperature profiles within the perturbed region is required. New diagnostics have to be developed to add significant new measure- ments relevant for these questions.
The experimental work should comprise the installation of new diagnostics on the tokamak TEXTOR (e.g. supersonic helium-beam, multi- pulse Thomson-scattering) providing a high temporal and spatial resolution, which allows in addition to the averaged profiles also the determination of fast processes at the plasma boundary [3,4]. A spatial resolution of about 5 mm and a temporal resolution of up to 100 kHz will allow to investigate in particular dynamic processes as they are caused by instabilities of the external distortion fields.
The accuracy of the data obtained from spectroscopic measurements relies among other issues on atomic data and collisional radiative modelling of the plasma. This issue will be addressed in cooperation with the Lebedev Instiute in Moscow (Prof. Vainshtein). The development of diagnostics is done in cooperation with the Budker Institute in Novosibirsk and the FOM Institute of Plasmaphysics in Rijhuizen.

References
[1] K.H. Finken (ed), Dynamic Ergodic Divertor (special issue) Fusion Eng. Design 37, 335 (1997)

[2] Ghendrih, P., Grosman, A., Capes, H., Plasma Phys. Contr. Fusion, 38, 1653 (1996)

[3] E Hintz and B Schweer, Plasma edge diagnostics by atomic beam supported emission spectroscopy - status and perspectives, Plasma Phys. Control. Fusion 37, A87 (1995), M. Brix, Messung von Elektronentemperatur und -dichte mittels Heliumstrahldiagnostik im Randschichtplasma eines Tokamaks, Berichte des Forschungszentrums Jülich; 3638 (1999)

[4] M.Yu Kantor, C.J. Barth, D.V. Kouprienko and H.J. van der Meiden, Test of a periodic multipass-intracavity laser system for the TEXTOR multiposition Thomson scattering diagnostics, Review of Scientific Instruments 72, 1159 (2001)

Investigation of the influence of ergodic field structures on impurity transport in magnetically confined high temperature plasmas

The dynamics of impurity transport can have significant impact on global plasma properties, like energy confinement, or local processes [1], like the growth of micro-instabilities. Therefore, the development of means to control impurity transport is of high interest within magnetic confinement fusion. In this context the new facility Dynamic Ergodic Divertor on TEXTOR [2], which allows to impose localised distortions on the confining magnetic field in order to modify plasma transport properties, is supposed to be such a tool.

Impurities have on the one hand to be minimised to avoid fuel dilution and thus reduced fusion power output in the plasma core, on the other hand, impurities are needed at the plasma boundary for enhancing the power output via line radiation from the plasma edge. Ergodic field structures can be an important means for optimising both aspects of impurity transport [3].

New diagnostics shall be used to investigate the new means for control of impurity transport, in particular, addressing the question of impurity screening by the edge plasma. Since these questions are related to former work with the ergodic divertor on the tokamak Tore Supra in Cadarache, a close cooperation with a group from CEA Cadarche and the University of Marseille is foreseen. Improvements of the beam technology are done in cooperation with the Budker Institute in Novosibirsk [4]. This project is of high interest for a later application on stellarators.

References
[1] Tokar M et al., Phys. Rev. Lett. 84, 895 (2000)

[2] K.H. Finken (ed), Dynamic Ergodic Divertor (special issue) Fusion Eng. Design 37, 335 (1997)

[3] Ghendrih, P., Grosman, A., Capes, H., Plasma Phys. Contr. Fusion, 38, 1653 (1996)

[4] A.A. Ivanov, V.I. Davydenko, P.P. Deichuli, A. Kreter, V.V. Mishagin, A.A. Podminogin, I.V. Shikhovtsev, B. Schweer and R. Uhlemann, Radio frequency ion source for plasma diagnostics in magnetic fusion experiments, Review of Scientific Instruments 71, 3728 (2000), A. Kreter, Ladungsaustauschspektroskopie mit Hilfe eines Wasserstoffdiag- nostikstrahls am Tokamak TEXTOR, Berichte des Forschungszentrums Jülich; 3860 (2001)

Models for fluctuation-induced transport and generation of transport barriers

An important and quite general topic of plasma physics is the relation between transport (of particles and heat) perpendicular to a magnetic field to the turbulence in plasmas. The latter may be of predominantly electrostatic nature, but also electromagnetic fluctuations could become important. Within the SFB 591 a specific aspect, namely transport in externally induced stochastic magnetic fields (as, e.g., being generated by the DED at TEXTOR), is being investigated. Here we would like to emphasize the complementary scenario, namely that the fluctuations build up during the development and saturation of instabilities [1]. Worldwide, very impressive measurements of fluctuation spectra are available. Also in Jülich correlations of fluctuations are measured with high spatial resolution [2]. It is planned to develop, in close collaboration with experiments, models for different excitations. The predictions of the models should be tested on the experimental results.

In more detail, we plan to generalize existing models [3] for low-frequency drift-waves, drift-Alfvén-waves, resistive ballooning modes, and magnetic islands resulting from non- linear tearing modes with the following steps:

• Systematic derivation of self-consistent fluid equations of a multi-species plasma including electrostatic as well as electromagnetic fluctuations


• Linear stability analysis


• Incorporation of gyro-kinetic effects


• Derivation of a reduced model for the nonlinear interaction of the most relevant modes [4,5]


• Comparison of the predictions of reduced descriptions with numerical simulations of the full set of equations. For the simulations we shall make use of existing codes which will be available either in Jülich directly or through collaborations with Bruce Scott (Garching/Düsseldorf), Volker Naulin (Risoe/Düsseldorf), Peter Beyer (Marseille), and Richard Sydora (Edmonton).


• Generation mechanisms for transport barriers between high- and low-temperature regions should be developed. Transport barriers (external as well as internal) have been observed in tokamak plasmas, but should also be present in astrophysical systems.

To our opinion, a thesis in this area will cover three important aspects: First, extensions of existing models should be able to interpret predictions of existing codes. Secondly, new experimental data will be available. Definitely, they will stimulate new interpretations. This will require theoretical work of high originality in the area of modelling physical systems. Results should qualify immediately for publication in a physical journal. Thirdly, an additional, more mathematically orientated aspect is worth mentioning. Recently, projection techniques have been discussed in the mathematical community [6]. These techniques may allow to identify the relevance of different modes in reduced models, i.e. to find arguments for the lowest dimension of a still physically relevant reduced model. If this works, it will provide us with a very efficient tool for comparing existing models and developing the most e±cient ones for mode-mode-interaction and transport barrier generation. The mathematical aspects of reduced modelling will be investigated together with the applied mathematics group.

The group has a long experience in anomalous transport calculations, fluctuation measurements, and numerical modelling. More information on the current status of research as well as the previous work of the applicants can be found, e.g., in the „Finanzierungsantrag 2003-2006 für den Sonderforschungsbereich 591 Universelles Verhalten gleichgewichtsferner Plasmen: Heizung, Transport und Strukturbildung".

References
[1] R. C. Wolf, Plasma Phys. Control. Fusion 45, R1 (2003)

[2] Krämer-Flecken, Trans. Fusion Techn. 37, 360 (2000)

[3] A. Rogister, Phys. Plasmas 7, 5070 (2000)

[4] P. Beyer and K. H. Spatschek, Phys. Plasmas 3, 995 (1996)

[5] M. Berning and K. H. Spatschek, Phys. Rev. E 62, 1162 (2000)

[6] A. J. Chorin, A. P. Hald, and R. Kupferman, Physica D 166, 3 (2002)

Nonlinear dynamics of laser driven and dissipative systems far from equilibrium

Localized structures are important objects of nonlinear dynamics in driven and dissipative systems far from equilibrium. The cubic, complex Ginzburg-Landau equation (CGLE) is one of the most-studied nonlinear models in such systems. It allows to understand a vast variety of phenomena, e.g. self-trapping of light, second-order phase transitions, superconductivity, superfluidity, Bose-Einstein condensation, liquid crystals, strings in field theory, particle acceleration in relativistic plasmas, and so on. In some areas, the CGLE appears as a generalized or higher-order nonlinear Schrödinger equation (HNLSE). The integrable (cubic) nonlinear Schrödinger equation (NLSE) is the weakly nonlinear and weakly dispersive paradigm for envelope radiation pulses. The nonlinear short pulse propagation requires further generalizations of the NLSE leading to a one dimensional CGLE or HNLSE by taking into account, e.g., dispersive-type higher order terms (such as third-order dispersion (TOD), nonlinear dispersion, and self-frequency shift (SFS) arising from stimulated Raman scattering). The models were further extended, particularly for intensive and short light pulses whose widths are shorter than 100 femtoseconds [1,2]. Then, not only the dispersive-type effects mentioned above, but also the driven and dissipative-type effects, such as spectral limitation due to gain bandwidth-limited amplification and (or) spectral filtering, nonlinear gain and (or) absorption with fast and (or) slow delayed nonlinear response, etc. may play important roles. Many authors have analyzed HNLSEs from different points of view, e.g. Painleve analysis, Hirota direct method, inverse scattering transform, Darboux-Bäcklund transform, etc. From the more practical point of view, the description of single-pulse propagation may be modelled by a Gauss-Hermite expansion or a variational approach [3] (also called variation of action method). Based on the latter approach, in the proposed work we shall try to develop a quasi-particle model.

It is a challenge to see whether it is possible to use a set of collective coordinates to represent the dynamics of the underlying in¯nite dimensional system. In more detail, we want to investigate the following topics:

• Arguments for the description of the single pulse dynamics in terms of the collective coordinates, such as amplitude, width, phase, chirp, frequency, and position.


• Comparison of the collective coordinate approach with simulations of the (full) original system [4].


• Stability criteria and classification of possible bifurcation scenarios in the presence of the physical effects mentioned above.


• Islands of complete integrability exist for certain parameter relations. The physical relevance of these islands should be worked out.


• Can we think of a system of many pulses as a system of many interacting quasi-particles? What is the relevant interaction potential?


• Incorporation of specific aspects of laser-plasma-interaction in the relativistic regime.

A central point of the indicated area of research is the use of the so called collective coordinates. Due to the introduction of a finite set of collective coordinates, an infinite- dimensional system will be significantly reduced. This reduction is often performed by physically motivated arguments. However, a more systematic mathematical procedure [5], based on projection techniques, is available. We have so far tested that procedure by introducing a reduced set of Fourier components as collective coordinates. It is important now to generalize the method in order to make contact with the physically motivated ansatz for collective coordinates. Thus, actually the proposed topic will result into two PhD theses, one being based on physically motivated questions, and the other on the mathematical background.

The group has a long experience in analytical and numerical modelling of nonlinear wave propagation. More information on the current status of research as well as the previous work of the applicants can be found, e.g., in the „Finanzierungsantrag 2004-2008 für den Transregio-Sonderforschungsbereich 18 Relativistic Laser Plasma Dynamics".

References
[1] Z. Li, L. Li, H. Tian, G. Zhou, and K.H. Spatschek, Phys. Rev. Lett. 89, 263901 (2002)

[2] J. A. Posth, T. Schäfer, E. W. Laedke, and K. H. Spatschek, Opt. Comm. 219, 241 (2003)

[3] D. Anderson, M. Lisak, and A. Berntson, Pramana 57, 917 (2001)

[4] M. Hochbruck and Ch. Lubich, SIAM J. Numer. Anal. 41, 945 (2003)

[5] A. J. Chorin, A. P. Kast, and R. Kupferman, Contemp. Math. AMS 238, 53 (1999)

Edge localised modes and their effect on global plasmas behaviour

Edge Localised Modes (ELMs), quasi-periodic crash-like variations of the transport in the edge transport barrier in tokamaks operating in the H-mode, affect the quality of the global plasma con¯nement and lead to a dangerous increase of particle and energy fluxes to the divertor plates in fusion devices. In order to describe these phenomena and to develop possible approaches to control ELMs, one needs theoretical models which, on the one hand, include the most essential physical mechanisms and, on the other hand, allow an effective coupling with complex transport codes providing afirm description of the global plasma behaviour.

The approaches proposed up to now normally include a relatively detailed description of MHD instabilities probably leading to ELMs (see, e.g., Ref. [1]) but fail in integration of this with a self-consistent description of the edge transport barrier. Such an integration is, however, of very importance since the characteristics of the barrier, i.e., its width, the plasma temperature on the top are essential for the overall discharge performance. A necessary selfconsistent description of the H-mode plasmas with edge barrier is now available with the code RITM (Radiation, Impurity, Transport Model) [2]. This code, permanently used and further developed in IPP-FZJ, has been successfully applied for interpretation of plasma behaviour under diverse discharge conditions in several fusion devices: radial detachment, radiation improved mode, effect of gas puffing on confinement in TEXTOR [3-5], effect of ergodic divertor in Tore-Supra [6], impurity seeding into JET [2,7], confinement improvement in RFX [8].

An amendment of the code RITM by a firm model for ELMs is a logical and unavoidable step in adaptation of RITM for modelling of reactor relevant conditions. A required model for ELMs should include the following important elements:

• An adequate description of plasma edge states between ELM events, i.e. in the H-mode phase before an ELM crash and in the L-mode phase after the crash


• A description of MHD instabilities and their effect on the transport at the edge through, e.g., ergodization of magnetic field lines during the crash


• Characterisation of the particle and energy transport in the scrape-off layer towards the divertor plates and their interconnection with the transport behaviour in the edge transport barrier


• Computation of time averaged transport coefficients


• Mechanisms to influence ELMs, e.g., through an artificial stochastization of magnetic field lines at the plasma edge

References
[1] P.Beyer and K. H.Spatschek, Center manifold theory for the dynamics of the L-H- transition, Phys. Plasmas 3, 995 (1996)

[2] B.Unterberg, D.Kalupin, M. Z.Tokar, G.Corrigan, P.Dumortier, A.Huber, S.Jachmich, M. Kempenaars, A.Kreter, A. M.Messiaen et al., Predictive modelling of the impact of argon injection on H-mode plasmas in JET with the RITM code, Plasma Phys. Control. Fusion 46, A241 (2004)

[3] M. Z. Tokar, Modelling of detachment in a limiter tokamak as a non-linear phe- nomenon caused by impurity radiation, Plasma Phys. Contr. Fusion 36, 1819 (1994)

[4] M. Z. Tokar, Edge-core interplay in transition to radiative improved mode, Contrib. to Plasma Phys., 38, 67 (1998)

[5] D. Kalupin, M. Z. Tokar, P. Dumortier, A. Messiaen, D. Reiter, S.Soldatov, B. Unterberg, G. van Wassenhove and R. Weynants, Modelling of confinement degradation in the radiative improved mode caused by a strong gas puff, Plasma Phys. Control. Fusion 43, 945 (2001)

[6] M. Z. Tokar, H. Lasaar, W. Mandl, W. R. Hess and C. de Michelis, Modelling of plasma and impurity behaviour in a tokamak with a stochastic layer, Plasma Phys. Control. Fusion 39, 569 (1997)

[7] M. Z. Tokar, H. Nordman, J. Weiland, J. Ongena, V. Parail, B. Unterberg and contributors to the EFDA-JET Workprogramme, Predictive modelling of impurity seeded plasmas in JET, Plasma Phys. Control. Fusion 44, 1903 (2002)

[8] G. Telesca and M. Z. Tokar, Modelling of PPCD in the reversed field pinch RFX by the transport code RITM, Nucl. Fusion 44, 303 (2004)

[9] H. Gerhauser, R. Zagorski, D. Reiter, M. Z. Tokar, Numerical modelling of changes of edge plasma transport due to the presence of TEXTOR-DED, to be published

Production of hot, dense plasmas using sub-ten femtosecond laser pulses

A hot, close to solid density plasma is an ideal matter to study radiative properties in the XUV spectral wavelength region that is of fundamental importance in astrophysics. In particular, the radiative opacity of the material in stellar interiors plays a key role in determining how stars evolve, what the maximum mass of a stable star is, how hot and how luminous the star is while it burns its hydrogen fuel. The opacity sets the flow of heat through the star. Opacity is very complex in this region and is a formidable challenge to theoretical atomic physics. Therefore the generation of dense plasmas with ultra-intense laser pulses is a field of enormous topical interest. An upper limit of the maximum plasma density that can be achieved with this method, however, occurs due to the formation of a preplasma and the expansion of the plasma during the interaction. Hence with nanosecond or even 100 fs laser pulses with prepulses the maximum plasma temperature is generally at about 10 times critical density. Several experimental studies have tried to overcome these shortcomings either by using time resolving x-ray spectroscopy or by using multilayered targets. For example time resolved x-ray emission spectroscopy on aluminium targets irradiated with a 12 ps Raman amplified KrF laser showed that hot plasmas with electron densities above 10²³ cm^-3 can be generated [1].

We recently used a novel approach that is based on a laser system that generates sub 10 fs pulses with a low prepulse energy [2]. Isochoric heating is demonstrated using small Z solid targets irradiated at an intensity of about 10¹⁶ Wcm^-2. Time integrated XUV spectroscopy was used to investigate K-shell emission from a carbon plasma. In the spectra, only the Ly alpha and He alpha lines are observed, whereas transitions from orbitals with principal quantum numbers n > 2 are not present. This series limit is explained by pressure ionisation in the dense plasma.

Here it is proposed to measure the line shapes of these two transitions, particularly the spectral bandwidth and the absolute wavelengths of the transitions. In addition, the satellites will be investigated [3]. The data will be invaluable for the refinement of the atomic physics models. The interpretation of the spectra will be carried out in close collaboration with Prof. S. Rose (University of Oxford) who is one of the leading experts in this area worldwide.

This project is ideally suited for a three year PhD programme. It includes the design and commissioning of a novel XUV spectrograph with a toroidal flat field reflection grating that has high spectral resolution, the calibration of the spectrogragh, detailed measurements of different plasmas (carbon, nitrogen, fluorine) produced by the sub-ten femtosecond laser and interpretation of the data in collaboration with Prof. Rose. The follow-on project will include detailed measurements of L-shell spectra of medium Z elements (Sc, Ti, Vd) [4] and in particular to study high density iron plasmas in the XUV spectral wavelength range. These measurements have great relevance for astrophysics.

References
[1] D. Riley, L. Gizzi, F. Khattak, A. Mackinnon, S. Viana and O. Willi, Plasma conditions generated by interaction of high brightness pre-pulse free Raman amplified KrF laser pulse, Phys. Rev. Lett. 69, 3739 (1992)

[2] J. Osterholz, T. Fischer, F. Brandl, G. Pretzler, O. Willi and S. Rose, Isochoric heating of low Z targets with sub 10 fs laser pulses, invited paper at the APS conference, 2004

[3] D. Riley and O. Willi, Observation of plasma satellite lines in laser produced plasmas, Phys. Rev. Lett. 75, 4039 (1995)

[4] J. Edwards, V. Barrow, O. Willi and S. Rose, Experimental observations of L and M-shell spectra emitted from plasmas produced by the irradiation of solid targets with single 3.5 ps KrF laser pulse, Appl. Phys. Lett. 57, 2086 (1990)

Interaction of intense radiation and particle sources with walls

One of the major problems for the diverters and walls of tokamaks will be the damage caused by the energetic particles (run-aways). The particles generated by ultra-short high intensity laser pulses have similar energies and are consequently ideally suited to simulate these fundamental damage issues.

Intense sources of hard radiation and energetic particles (electrons, ions, protons, neutrons) are produced during the interaction of high power laser pulses with matter. For example, particles with a density of 10¹² cm^-3, with energies in the MeV range are generated in these short pulses, high intensity interaction experiments. In particular, electrons and ions are very directional with a cone angle of about 15 degrees and hence can be used to study the wall loading and wall lifetimes very localised. These measurements will be carried out at the HHUD using the OPCPA laser system and on larger laser facilities allowing scaling laws to be obtained.

In detail, it is proposed to study the interaction of ions and electrons (between hundreds of keV and MeV) produced in high intensity laser pulse experiments with various materials. In particular, the deposition and heating in solid materials simulating the wall of a tokamak will be measured using XUV and soft x-ray emission spectroscopy. Multilayered targets with thin tracer layers will be used to measure the deposition depth and the heating of the fast particles in the layers.

Although the proton, ion and electron emission from high intensity laser interaction with thin foil targets is understood [1,2], the interaction of these intense sources on separate targets has not been studied so far and hence is suited for a PhD project with a three years duration. This research will be carried out in cooperation with our Jülich colleagues and Dr. M. Borghesi (Belfast, UK). The follow-on project will develop diagnostic packages consisting of multilayered targets that will be used on the wall of a tokamak to measure the interaction of fast particles.

References
[1] A. J. Mackinnon, M. Borghesi, S. Hatchett, M. H. Key, P. K. Patel, H. Campbell, A. Schiavi, R. Snavely, S. C. Wilks, and O. Willi, Effect of Plasma Scale Length on Multi-MeV Proton Production by Intense Laser Pulses, Phys. Rev. Lett. 86, 1769 (2001)

[2] M. Borghesi, A. J. Mackinnon, D. H. Campbell, D. Hicks, S. Kar, P. K. Patel, D. Price, L. Romagnani, A. Schiavi, and O. Willi, Multi-MeV proton source investigations in ultraintense laser-foil interactions, Phys. Rev. Lett. 92, 055003/1 (2004)

Resonant MHD coupling of external helical magnetic field perturbations in tokamak plasmas

Helical magnetic field perturbations are introduced in tokamak plasmas to study, on the one hand, the ergodic divertor concept, and, on the other hand, the interaction of such perturbations with the magneto-hydro-dynamic (MHD) stability of the plasma. Recent collaborative experiments at the DIII-D tokamak (General Atomics, San Diego, California, USA) suggest a control method to mitigate edge localized modes while maintaining the pedestal pressure and thus plasma confinement [1]. However, open questions remain also with regard to the influence on plasma stability.

The Dynamic Ergodic Divertor (DED) in the TEXTOR [2] tokamak imposes an externally created perturbation of the magnetic field. As a consequence the magnetic field becomes ergodized and magnetic islands are created, even in plasmas where these instabilities are naturally stable. A unique feature of the DED experiment is that the perturbation field can be rotated with frequencies of up to 10 kHz. The perturbation coils of the DED can generate magnetic fields with both high (m/n = 12/4) and low (m/n = 3/1) principal mode numbers which are resonant to specific magnetic flux sur- faces. Owing to the coupling of the DED to the plasma and the corresponding magnetic field ergodization, the transfer of torque to the plasma and changes of the plasma wall interaction, modifications of both plasma transport and stability are expected [3].

First experiments with the DED in m/n = 3/1 mode configuration [4] have shown that in static operation a m/n = 2/1 tearing mode is created above a critical perturbation field amplitude. Due to the applied static field this mode does not rotate and the plasma rotation breaks down. A similar behaviour was found with 1 kHz dynamic operation when the perturbation field rotates in direction of the plasma current (co-rotation). In counter-rotation the mode is excited at a significantly larger perturbation field amplitude, or is not excited at all [5].

Investigations of the dependence of the critical field amplitude on various plasma parameters yield a surprising relation between the critical perturbation field and the toroidal plasma rotation velocity [4]: Contrary to initial expectations, an increase of the toroidal rotation due to an enhancement of the tangential neutral beam injection (and keeping the total heating power constant by a reduction of the ion cyclotron resonance heating power) results in a decrease of the critical field amplitude required to excite the mode.

Within the scope of this work detailed investigations of parametric dependencies of the mode onset should be explored. Especially the influence of plasma rotation can be precisely studied using the co- and counter-current directed neutral beam injection systems on TEXTOR. For the interpretation of the experimental results it is planned to apply a version of MHD stability code CASTOR, which has been further developed at the Max-Planck-Institut für Plasmaphysik in Garching, taking the influence of plasma rotation into account.

Possible extensions of this work are experiments which address plasmas with small internal inductance and as high as possible plasma pressure. In this kind of discharges external kink modes are supposed to become unstable. These ideal MHD modes represent a limitation of the operational domain in high beta plasmas with internal transport barriers [6]. It is anticipated to suppress or stabilize them by a combination of a closely fitting conducting wall and external coil systems. The flexible neutral beam heating system on TEXTOR and the external perturbation field created by the DED will allow well defined experiments to be performed and to gain knowledge on the feasibility of such active stabilization.

References
[1] T. Evans, R. Moyer, P. Thomas et al., Phys. Rev. Lett. 235003 (2004)

[2] K. H. Finken (Guest Editor), Special Issue: Dynamic Ergodic Divertor, Fusion Engineering and Design 37, 337 (1997)

[3] K. H. Finken, Nucl. Fusion 39, 707 (1999)

[4] K. H. Finken, S. S. Abdullaev, M. F. M. de Bock, M. Von Hellermann, M. Jakubowski, R. Jaspers, H. R. Koslowski, A. Krämer-Flecken, M. Lehnen, Y. Liang, A. Nicolai, R. C. Wolf et al., Toroidal plasma rotation induced by the Dynamic Ergodic Divertor in the TEXTOR tokamak, submitted to Phys. Rev. Lett. (2004)

[5] H. R. Koslowski, A. Krämer-Flecken, Y. Liang, O. Zimmermann, K. H. Finken, M. von Hellermann, R. Jaspers, E. Westerhof, R. C. Wolf, Proc. 31st Eur. Phys. Soc. Conf. on Plasma Physics, London (June 2004) P1.124

[6] R. C. Wolf, Plasma Phys. Control. Fusion 45, R1 (2003)