Another PFM used in fusion devices is beryllium. Although the beryllium crystal
structure, hexagonal close-packed, is very different from the body-centered cubic
lattice of tungsten, the DFT simulations show that only up to five hydrogen atoms
could be trapped in a beryllium lattice vacancy with the de-trapping energy ~1.7 eV
[105, 106]. The trapping energies from 1.25 to 2 eV were also deduced from the
analysis of the TDS data (e.g. see [107]). However, unlike tungsten where the
amount of trapped hydrogen is increasing with Φ H [65], the amount of hydrogen
retained in beryllium saturates with Φ H at a relatively low value [101, 108]. This is
probably due to the formation of interconnected hydrogen nano-bubbles creating a
porous structure in a rather thin sub-surface layer [108–110]. However, due to
relatively high erosion of beryllium, the beryllium co-deposits (formed from the
eroded beryllium atoms transported to and deposited at some particular locations in
fusion devices) are the main sources of retained hydrogen in beryllium-containing
tokamaks such as JET [3, 40, 101]. Similarly, for the case of carbon-based tokamaks,
the main reservoir of retained hydrogen was in the carbon co-deposits (e.g. see [2]
and the references therein). According to [40, 111], beryllium co-deposits formed at
relatively low temperature have an amorphous structure.
Interestingly, the hydrogen outgassing flux from the PFM at a constant temperature, Γ out , from different tokamaks with both beryllium and carbon co-deposits
exhibit (varying by orders of magnitude) similar temporal dependence Γ out (t) / t
Àα
with α % 0.7 [3, 112–114]. Whereas the tokamak data could be related to some
peculiarities of wall loading with hydrogen, the laboratory experiments with a
constant deposition rate also demonstrate the power-law temporal dependence of
Γ out (t) with similar values of α [115]. We notice that the standard diffusion law
would give α ¼ 0.5. The physical reason for such an unexpected dependence of
Γ out (t) is not clear. It is plausible that the amorphous co-deposits have a rather broad
band of hydrogen trapping energies so that hydrogen transport can finally be
described with fractional diffusion equations resulting in α 6 ¼ 0.5 [46].
However, during a discharge, both the hydrogen outgassing flux from the PFM
and the wall uptake have a much more complex temporal behavior [116, 117]. As an
example, from Fig. 3.12 one can see, how the dynamic particle (hydrogen) exchange
between the plasma and the wall structures during a discharge in the JET tokamak
actually works.
Finally, we discuss briefly the usage of lithium as the material for the PFCs
(e.g. see [22] and the references therein). Lithium (both solid and liquid) is used for
the PFCs in fusion-related experiments (including tokamaks [118–122]) for more
than a decade. One of the clear advantages of lithium is low Z, which makes it rather
benign from the point of view of plasma contamination. It is difficult to predict,
whether lithium will be used in future fusion devices (but see [123]), but these days
lithium becomes more and more popular in the fusion community as, at least, a tool
for improving tokamak performance and solving some current issues with the PFM.
Liquid lithium is a subject of both Bénard-Marangoni convection (caused by
temperature-dependent surface tension) and j
! Â B
!
force, where the electric current
j
!
can be driven by both the plasma and the thermoelectric effects. The latter ones
64
3 Plasma-Material Interactions in Magnetic Fusion Devices
structure, hexagonal close-packed, is very different from the body-centered cubic
lattice of tungsten, the DFT simulations show that only up to five hydrogen atoms
could be trapped in a beryllium lattice vacancy with the de-trapping energy ~1.7 eV
[105, 106]. The trapping energies from 1.25 to 2 eV were also deduced from the
analysis of the TDS data (e.g. see [107]). However, unlike tungsten where the
amount of trapped hydrogen is increasing with Φ H [65], the amount of hydrogen
retained in beryllium saturates with Φ H at a relatively low value [101, 108]. This is
probably due to the formation of interconnected hydrogen nano-bubbles creating a
porous structure in a rather thin sub-surface layer [108–110]. However, due to
relatively high erosion of beryllium, the beryllium co-deposits (formed from the
eroded beryllium atoms transported to and deposited at some particular locations in
fusion devices) are the main sources of retained hydrogen in beryllium-containing
tokamaks such as JET [3, 40, 101]. Similarly, for the case of carbon-based tokamaks,
the main reservoir of retained hydrogen was in the carbon co-deposits (e.g. see [2]
and the references therein). According to [40, 111], beryllium co-deposits formed at
relatively low temperature have an amorphous structure.
Interestingly, the hydrogen outgassing flux from the PFM at a constant temperature, Γ out , from different tokamaks with both beryllium and carbon co-deposits
exhibit (varying by orders of magnitude) similar temporal dependence Γ out (t) / t
Àα
with α % 0.7 [3, 112–114]. Whereas the tokamak data could be related to some
peculiarities of wall loading with hydrogen, the laboratory experiments with a
constant deposition rate also demonstrate the power-law temporal dependence of
Γ out (t) with similar values of α [115]. We notice that the standard diffusion law
would give α ¼ 0.5. The physical reason for such an unexpected dependence of
Γ out (t) is not clear. It is plausible that the amorphous co-deposits have a rather broad
band of hydrogen trapping energies so that hydrogen transport can finally be
described with fractional diffusion equations resulting in α 6 ¼ 0.5 [46].
However, during a discharge, both the hydrogen outgassing flux from the PFM
and the wall uptake have a much more complex temporal behavior [116, 117]. As an
example, from Fig. 3.12 one can see, how the dynamic particle (hydrogen) exchange
between the plasma and the wall structures during a discharge in the JET tokamak
actually works.
Finally, we discuss briefly the usage of lithium as the material for the PFCs
(e.g. see [22] and the references therein). Lithium (both solid and liquid) is used for
the PFCs in fusion-related experiments (including tokamaks [118–122]) for more
than a decade. One of the clear advantages of lithium is low Z, which makes it rather
benign from the point of view of plasma contamination. It is difficult to predict,
whether lithium will be used in future fusion devices (but see [123]), but these days
lithium becomes more and more popular in the fusion community as, at least, a tool
for improving tokamak performance and solving some current issues with the PFM.
Liquid lithium is a subject of both Bénard-Marangoni convection (caused by
temperature-dependent surface tension) and j
! Â B
!
force, where the electric current
j
!
can be driven by both the plasma and the thermoelectric effects. The latter ones
64
3 Plasma-Material Interactions in Magnetic Fusion Devices