Attenuation of the ion flux on the CFC protective housing 

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Rotating double probe

A rotating double probe for SOL i T measurements was proposed by Höthker and used in TEXTOR tokamak [Höthker 1990]. The probe consists of two symmetric cylindrical pins, 5 mm in diameter and length, separated by 10 mm. During the discharge the system rotates around its axis which is perpendicular to B with a frequency of 2 Hz.
The ion saturation current collected by probe pins showed a dependence on the angle of rotation, reaching a minimum value when the pins magnetically shadow each other. In [Höthker 1990] the observed ion current modulation with the rotation angle was associated with finite ion Larmor radius effects and studied by Monte Carlo simulations. i T was determined by fitting a calculated profile of the collected particle flux to the measured ion saturation current profiles.
The accuracy of i T measurements could be, however, affected by simplifications used in the Monte Carlo simulations. For example, the model assumes a simple Maxwellian distribution (i.e. it neglects the pre-sheath effects on the parallel ion velocity distribution) and neglects the space charge effects [Höthker 1990]. Some other effects that can influence i T measurements are discussed in [Höthker 1990] and the authors claim the error on i T is around 30%. Obviously, measurement of the radial profile of SOL i T by the rotating probe mounted on a fast reciprocating drive will be technically challenging since much higher rotation frequencies will be required.A similar double probe with asymmetric electrodes [Amemiya 1989, Maeda 1997, Amemiya 1994] as well as the rotating double probe with symmetric and asymmetric electrodes [Uehara 1998] were used to measure i T in the JFT-2 tokamak.

Fusion power plant

The tokamak reactor can be used for production of energy in two ways: as a “pure” fusion power plant or as a part of a hybrid fission-fusion power plant. While the first is currently the mainstream of the fusion research because of its attractiveness with regards to environmental and safety issues, the latter might be easier to put into practice in the not too distant future.
Compared to the current experimental devices, a “pure” fusion power plant with tokamak reactor will require additional elements in order to convert the fusion power into electricity. The vacuum vessel will be surrounded by a blanket that will (i) absorb the energy of the neutrons from the fusion reactions and transform it to heat carried away by a coolant, (ii) protect the outer components of the reactor from the neutron flux and (iii) allow for breeding of tritium to fuel the reactions. This may be accomplished by composing the blanket of Li2O. Additional elements like e.g. the blanket coolant, heat exchanger, turbine and the generator will be needed. Since the tokamak transformer action can drive the electric field only for limited period, the reactor will work in pulsed operation. Alternatively, continuous current drive could be provided by combining the bootstrap current produced by plasma itself with that produced by injection of the neutral particle beams or electromagnetic waves.
The idea of the hybrid fission-fusion reactor is to surround the fusion reactor with a blanket of abundant “fertile” materials such as uranium-238 or thorium-232. Fast neutrons produced in D-T reactions in the tokamak plasma will convert these materials into fissile isotopes (uranium-233 or plutonium-239). The fissile material will then be used as a fuel for ordinary fission reactors. The fission-fusion power plant should consist of a relatively small (Q = 2 − 5) pulsed tokamak (i.e. current drive might not be necessary) that could breed enough fuel for several satellite fission reactors. The feasibility of the hybrid fission-fusion systems has been addressed e.g. in [Bethe 1979, Nifnecker 1999, Gohar 2001, Hoffman 2002, Stacey 2002]. The fusion-fission hybrid system has potential attractiveness because of the large amount of produced energy and the abundance of fuel available compared to the fission reactor. Hybrid reactors are expected to be able to provide energy for more than 10000 years, giving a comfortable fuel assurance. The conditions for making such reactors economical may be considerably less stringent than those for fusion reactors producing electric power alone. Hybrids seem to be a practical path to the early application of fusion for energy production and would provide enough time to continue the progress towards pure fusion reactor, which is now many years away. However, apart of the political and public objections that the hybrid concept will probably provoke (because of the risk of proliferation as well as the fact that hybrid reactors involve nuclear fission), a number of technical issues needs to be solved. This includes e.g. the increase of the neutron fluence, the problems related to the first wall materials, and the design of the fissile fuel breeding blanket.

Plasma boundary in tokamaks

In tokamaks all four states of matter (solid walls of the vessel, liquid melting layer, gas consisting of neutral atoms, as well as plasma consisting of ionized atoms, molecules, and electrons) interact in a very small space. The transition between the plasma and the outer world is the biggest challenge of controlled fusion. The interaction of plasma with first-wall surfaces will have a considerable impact on the performance of fusion plasmas, the lifetime of plasma facing components and the retention of tritium in the next step experiment ITER.
In addition to the motion along B, magnetically confined charged particles diffuse across magnetic field lines from the confining region towards the inner wall of the vacuum vessel. The interaction of the charged particles with the material wall leads to the production of impurities and subsequent dilution of the plasma. In addition, large concentrated heat fluxes from the plasma can damage (i.e. by melting, sputtering, or brittle destruction) the plasma facing components. If the first wall were parallel with B at every point, the total radial heat flux from the plasma would be dissipated over large area, leading to very low heat flux densities. However, such a configuration could not be built in reality because of the finite edges of the wall tiles, diagnostic ports, screws, etc. that must inevitably appear. Another reason why the uniform distribution of the incident heat flux density could not be achieved is that the particle and energy fluxes from the plasma are poloidally non-uniform (e.g. [Asakura 2007, Kočan 2009] because of the curvature of the magnetic field lines. In addition, fast particles can be detrapped from the magnetic ripple wells due to the finite number of the toroidal magnetic field coils [Basiuk 2001], leading to a localized damage of the inner vessel components. Therefore, instead of bringing the whole plasma surface in contact with the material surface, tokamak plasmas are separated as much as possible from the vessel wall.
The simplest and oldest method to separate the tokamak plasma from the vessel wall is to insert an annulus of solid material called a “limiter”. Limiters can be either discrete or continuous in the toroidal or poloidal direction. Curved inner walls of the vessel covered by protective tiles are used as a wall-limiter. Additional limiters are used to protect the RF heating antennas . In fact, any object that is inserted into the plasma and is large enough (see section 1.2.4.2) acts as a limiter. Obviously, the price paid for the separation of the first wall from the plasma by means of a limiter is in the high flux densities to the limiter surface.
The poloidal cross-section of a limiter tokamak is shown in figure 1.8. The magnetic field lines which lie on flux surfaces that are not in contact with the limiter are termed “closed”. Those which intersect a solid surface are termed “open”. The outermost flux surface with closed magnetic field lines is termed “last closed flux surface” (LCFS). LCFS separates the “confined” region (being the region inside the LCFS) from the scrape-off layer (SOL) which is localized outside the LCFS (more accurate definition of the SOL is given in section 1.2.2.1).
Once inside the SOL, the particles move along the field lines towards the limiter strike zones. Because the parallel movement of particles (which in this thesis coincides with the movement along B) is much faster compared to the perpendicular movement, the particles only have time to diffuse a short distance beyond the LCFS – typically a few centimetres in large tokamaks, section 1.2.2.1. The limiter thus effectively separates the vessel wall from the plasma. On the other hand, since the limiter strike zones are much smaller compared to the total vessel wall, the heat flux from the plasma is concentrated on a smaller area. This may result in large heat flux densities to the limiter because of localized power deposition. Although separated from the main vessel wall, the confined plasma is in fact in direct contact with the limiter. Therefore, there is high probability that the impurities produced by the impact of charged particles from the plasma onto the limiter surface will enter directly the confined region.
More appropriate in the control of the plasma dilution by impurities is the magnetic divertor. The divertor is produced by an additional toroidal coil, which, together with the plasma current, produces a figure-of-eight shape of the magnetic field in the poloidal plane, figure 1.8. Plasma sink is achieved by intersecting the flux surface around the additional coil by solid plates (divertor targets). The magnetic flux surface passing through the X-point is called the “separatrix”. The SOL is localized outside the separatrix, except the region between the X-point legs which is called the “private flux region”. In divertor configuration the plasma wetted area is separated from the confined region which makes it easier to maintain lower impurity level in the plasma. This is because the impurities sputtered from the divertor plates are ionized more likely in the SOL (so that they can return to the wall along the open field lines) and are less likely to enter the confined plasma compared to the limiter configuration. The divertor also provides optimized plasma shape and allows for exploring possible advantages of the small aspect ratio. On the other hand, the divertor configuration is less efficient in the use of magnetic volume.

The Debye sheath

Because of the large difference in the ion and electron mass, a potential drop – the Debye sheath – spontaneously arises between the plasma and the solid surface (such as the limiter target or probe). It can be shown (e.g. [Stangeby 2000]) that the characteristic scale length of the Debye sheath is the Debye length λD = ε0Te / en (with Te in eV). Typically λD ≈ 10 µm in the tokamak SOL.
To have a non-oscillatory solution of Poisson’s equation for the electric potential in the Debye sheath requires ions to enter it with parallel velocity v// ≥cs (1.8).
where cs = e(Ti + Te ) / mi is the ion sound speed. Eq.(1.8) is referred to as generalized Bohm criterion [Allen 1976].
The potential drop in the Debye sheath can be obtained from the equation for the net (ion and electron) current to the surface which needs to be zero ji + je = 0 . The sheath is assumed to be sourceless so that the ion current is conserved through the sheath. The ion current to the surface is ji = nseecs (with nse being the electron density at the sheath entrance or “sheath edge”). Neglecting secondary electron emission from the surface and assuming Boltzmann electrons, the electron current to the surface j e = 1 n se ec e exp(eV /T ) where c = 8T /πm is the average electron speed and V is 4 0 e e e e 0 22 q// = γTeΓ// , the potential of the surface (with Vse = 0). Hence the potential drop between the sheath edge and the electrically floating surface e m 1+ T . i e T m T Vsf = 0.5 e ln 2π e i (1.9).
Again, Eq.(1.9) is derived assuming zero secondary electron emission from the surface. Allowing for secondary electron emission, additional factor of (1− δ )−2 (with δ being the secondary electron emission coefficient) will appear inside the logarithm. Vsf decreases with the increase of Ti /Te and δ , and with the decrease of ion mass. Vsf ≅ 3Te for Ti = Te , δ = 0 and mi = mD (where mD is the deuteron mass). The existence of the sheath has an important consequence for plasma-wall interactions: in the sheath the kinetic energy of ions is increased by eZiVsf and can thus exceed the threshold for the physical sputtering, increasing the impurity production rate.

The heat flux density and the heat transmission coefficient

The parallel heat flux density q// in the SOL plays a key role in the determination of the power loads on the plasma-facing components in tokamaks. (1.10).
where γ is the total (ion and electron) heath transmission coefficient. γ Te is thus the amount of heat [W] removed from plasma per each ion-electron pair. Γ// is equivalent to jsat / e , the parallel ion current density which, together with Te , is directly accessible by Langmuir probes, section 1.2.4. The details of the derivation of the heat transmission coefficient can be found e.g. in [Stangeby 2000b]. We state here only the final relation which is derived for electrically floating surface and assuming that the floating potential is negligible compared to Vsf : 2.5T m T −2 2 i e im 1+ T (1−δ) + e i e γ ≅ T − 0.5ln 2π 1−δ . (1.11).
δ is again the secondary electron emission coefficient which includes true secondary as well as reflected electrons. First term on the RHS of Eq.(1.11) accounts for the kinetic energy of ions increased by the sheath acceleration. Te in the denominator of the first term is due to the fact that q// in Eq.(1.11) is scaled in Te . The remaining two terms account for the kinetic energy of electrons. 1− δ in the denominator of the third term appears because of the secondary electrons re-injected into the plasma (either true secondary electrons or reflected ones). The heat flux density of the Maxwellian electrons to the wall qe = (2Te −Vsf ) je +Vsf jsec with je being the electron current density to the wall and jsec being the current density of the secondary electrons re-injected into the plasma. Vsf (with Vsf < 0 , Eq. (1.9)) accounts for the deceleration (acceleration) of the incident (secondary) electrons in the Debye sheath. Since the net ion and electron current densities to the walls are equal (section 1.2.2.2), jsat = jnet with jnet = je (1−δ ) so that the electron component of the heat flux density to the wall can be written as qe = γ eTe jnet with γ e = 2 /(1− δ ) − Vs /Te . At fixed jsat , higher δ coincides with higher je (i.e. higher electron heat flux density to the wall). This is why 1− δ appears in the denominator of Eq.(1.11) and why γ (Eq.(1.11)) increases with δ . In figure 1.10, γ is plotted against Ti /Te . For example, within the typical range of SOL Γ// and Te in most tokamaks (1022 – 1024 m-2, 10-100 eV) q // ≅ 0.07 → 70MW m-2 for T = T and q // ≅ 0.14 → 140 MW m-2 i e for Ti = 4Te .

The importance of SOL Ti measurements

The ion temperature Ti in the tokamak SOL is of key importance for modelling plasma surface interaction processes such as physical sputtering, reflection and impurity release, estimation of the amount of the heat flux deposited on the divertor tiles and main chamber walls, calculation of the importance of the classical drift flows compared to turbulence driven flows, etc. These are critical parameters for designing tokamak plasma facing components. In addition, the ion temperature at the LCFS is, in addition to Te , an important boundary condition for core modelling.
It is often argued that SOL Ti is very difficult to measure compared to the SOL Te (which is accessible by a simple Langmuir probes) and the measurements of SOL Ti are therefore not available. In the models, the lack of Ti measurements is often followed by the assumption Ti = Te (e.g. [Federici 2007]). In some cases, experimentally measured edge temperature profiles are arbitrarily shifted radially to make the two temperatures agree [Saarelma 2005] and to make the model consistent with this assumption.
Most models are relatively sensitive to the exact value of the ion-to-electron temperature ratio and a significant error can be therefore anticipated if, in reality, Ti and Te are not equal. One example is the calculation of the parallel heat flux density in the SOL q// , Eq.(1.10). As shown in section 1.2.2.3., q// is proportional to the heat transmission coefficient which increases with Ti /Te , Eq.(1.11). For example, Ti = 4Te would imply two times higher q// compared to Ti = Te . Another example is the calculation of the electron density which is inversely proportional to the ion sound speed cs so that ne ∝ (Ti + Te )−1/ 2 . Ti plays a role in the estimation of the pressure driven (Pfirsch-Schlüter) flows (e.g. [Asakura 2000, Pitts 2007]) which are proportional to the ion pressure, in the estimation of the physical sputtering rates, etc.
It is true that SOL Ti cannot be measured like Te by a simple electrode swept with respect to the plasma potential. However, several techniques have been developed for SOL Ti measurements and successfully applied in many tokamaks (see references below and in section 1.4.2). Also true is that the database of SOL Ti measurements is very limited, but sporadic measurements of SOL Ti were already reported from most tokamaks like e.g.
• Alcator C [Wan 1986].
• ASDEX (Upgrade) [Staib 1980, Staib 1982, Reich 2004, Reich 2004b].
• CASTOR [Kočan 2005, Kočan 2006, Kočan 2007, Adamek 2008].
• DITE [Erents 1982, Stangeby 1983, Pitts 1989, Matthews 1991, Pitts 1991, Pitts 1996].
• JET [Guo 1996, Pitts 2003].
• JFT-2M [Uehara 1998].

Rotating double probe

A rotating double probe for SOL Ti measurements was proposed by Höthker and used in TEXTOR tokamak [Höthker 1990]. The probe consists of two symmetric cylindrical pins, 5 mm in diameter and length, separated by 10 mm. During the discharge the system rotates around its axis which is perpendicular to B with a frequency of 2 Hz.
The ion saturation current collected by probe pins showed a dependence on the angle of rotation, reaching a minimum value when the pins magnetically shadow each other. In [Höthker 1990] the observed ion current modulation with the rotation angle was associated with finite ion Larmor radius effects and studied by Monte Carlo simulations. Ti was determined by fitting a calculated profile of the collected particle flux to the measured ion saturation current profiles.
The accuracy of Ti measurements could be, however, affected by simplifications used in the Monte Carlo simulations. For example, the model assumes a simple Maxwellian distribution (i.e. it neglects the pre-sheath effects on the parallel ion velocity distribution) and neglects the space charge effects [Höthker 1990]. Some other effects that can influence Ti measurements are discussed in [Höthker 1990] and the authors claim the error on Ti is around 30%. Obviously, measurement of the radial profile of SOL Ti by the rotating probe mounted on a fast reciprocating drive will be technically challenging since much higher rotation frequencies will be required.
A similar double probe with asymmetric electrodes [Amemiya 1989, Maeda 1997, Amemiya 1994] as well as the rotating double probe with symmetric and asymmetric electrodes [Uehara 1998] were used to measure Ti in the JFT-2 tokamak.

Plasma ion mass spectrometers (PIMS)

Three types of mass spectrometers, used in the tokamak plasma boundary to measure the charge state distribution of impurities, are usually referred to as “180°” [Kojima 1984], “omegatron” [Nachtrieb 2000, Nachtrieb 2000b], and “cycloidal focusing” [Matthews 1989, Matthews 1990] spectrometers.
Only two of them, omegatron used in Alcator-C MOD and cycloidal focusing PIMS used in DITE, can also measure the ion temperature. Omegtron PIMS utilizes the RFA principle (Chapter 2) to measure Ti and is therefore irrelevant to this section.
DITE PIMS is based on the principle of cycloidal focusing [Matthews 1989, Matthews 1990] which is produced by perpendicular magnetic and electric fields inside the probe cavity. The electric field is produced by two parallel plates. The ions enter the probe through a thin aperture (width of λD ) and are focused onto an array of three electrically insulated collectors that are parallel to B. The principal application of the DITE PIMS is the measurement of the charge state distribution of SOL ions, which is inferred from the mass spectra obtained by ramping the electric field in time to sweep the various foci across the collector array.
The measurements of Ti by PIMS are similar to that of the E×B probe. Since the ions have different parallel energies, their cycloids are stretched along the collectors. The collector currents can be used to measure f (Ei // ) . The ion temperature is obtained from the least squares fit of the distributions calculated by Monte Carlo simulations to the experimental collector current ratios. In Monte Carlo simulations it is assumed that the different charge state distributions are isothermal, isotropic and Maxwellian with a velocity shift associated with the Debye sheath acceleration [Matthews 1991]. Since the ion energy distribution at the sheath edge in front of the probe is known to be perturbed by the presence of the probe combined with the plasma flow [Chung 1988] such assumptions could provide only very approximate values of Ti .

Langmuir probe with a thermocouple

The probe consists of a thermocouple that works simultaneously as a Langmuir probe. The analysis of the measured data is carried as follows:
(i) The Langmuir probe provides the measurements of Te and Isat .
(ii) The thermocouple measures the incident power P .
(iii) Assuming that P = AIsat E(Ti ,Te ) (with A being the thermocouple area and.
E(Ti ,Te ) the energy transferred to the thermocouple per one ion-electron pair) Ti , the only unknown, can be obtained by an iterative process.
The probe was successfully used in the SOL of DITE [Stangeby 1983] and PLT [Manos 1982]. The advantage of this probe is in its relative simplicity and robustness. In addition, the measurements of Ti , Te and Isat provide also the information about the SOL electron density, ne ∝ Isat / cs (Ti ,Te ) .
On the other hand, E(Ti ,Te ) is calculated using a simple sheath theory for Maxwellian electrons and singly charged ions [Stangeby 1983] and is a function of other parameters that are not measured (e.g. the coefficient of the secondary electron emission from the thermocouple surface). Moreover, the statistical error on Ti includes the errors on Te , Isat and P and can be, therefore, relatively large.

Table of contents :

Chapter 1 – Introduction
Basic principle of magnetic confinement fusion
Why fusion
The principle of the nuclear fusion
Ignition
Magnetic confinement fusion
Tokamak
Progress in the tokamak research
ITER
Fusion power plant
Plasma boundary in tokamaks
Impurities
Limiter SOL
Radial drop of density and temperature in the SOL
The Debye sheath
The heat flux density and the heat transmission coefficient
Parallel density and potential gradients in the pre-sheath
Langmuir probes
Mach probe
Disturbance of the plasma by probe insertion
Tore Supra
Ion temperature measurements in the tokamak plasma boundary
The importance of SOL Ti measurements
Techniques for SOL Ti measurements
Ratynskaia probe
Katsumata probe
Rotating double probe
E×B probe
Plasma ion mass spectrometer (PIMS)
Langmuir probe with a thermocouple
Thermal desorption probe
Carbon resistance probe
Surface collection probe
Charge exchange recombination spectroscopy
Chapter 2 – Retarding field analyzer 
RFA in the tokamak plasma boundary
RFA principle
Tore Supra RFA
Probe design, electronics, operation and data analysis
Probe design
Electronics
Operation and data analysis
Instrumental study of the Tore Supra RFA
Attenuation of the ion flux on the CFC protective housing
Background of the ion current attenuation
Tunnel probe
Particle-in-cell simulations
Comparison of experimental data, theory and PIC simulations
Attenuation of the ion flux on the protective plate
Ion transmission through the entrance slit
Theoretical model of ion transmission through the slit
PIC simulations of the ion transmission through the slit
Deformation of I-V characteristics
The relative slit transmission factor
Space charge effects
Influence of the negatively biased grid
Some remarks on the error on Vs and Ti due to the fit to the measured
Introduction
Analysis of the artificial I-V characteristics
Annex
Chapter 3 – Experimental results 
M. Kočan et al 2008 Plasma Phys. Control. Fusion 50 125009
M. Kočan et al 2009 J. Nucl. Mater. 390-391 1074
M. Kočan et al 2009 submitted to Plasma Phys. Control. Fusion
M. Kočan and J. P. Gunn 2009 to be published in the Proc. 36th EPS Conference on Plasma Physics (Sofia, June 29 – July 3)
Chapter 4 – Three projects to validate Ti measurements in Tore Supra 
Edge ion-to-electron temperature ration in the L-mode plasma in JET
Introduction
JET L-mode database of edge Ti and Te
Preliminary results
Comparison of the SOL Ti measured by the RFA and by the CXRS in Tore Supra
The segmented tunnel probe for Tore Supra plasma boundary
Introduction
STP principle
A prototype STP tested in the tokamak CASTOR
Tore Supra STP
Probe design
Probe calibration
Experimental data
Measurements of the large floating potentials in the ICRH power scan
Conclusions
References

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