Technical Design Report Super Fragment Separator

DRAFT
Like in the case of the rotating graphite wheel it is of great interest to apply the conditions of the
windowless liquid target with enlarged beam spots. Calculations with BIG-2 for 1 A GeV 10 12 238 U
ions / 50 ns with a spot area of σx = 2 mm and σy = 12 mm impinging on the liquid lithium target
[64] demonstrate that after 1 µs the target remains liquid (density changes only by 0.04 g/cm 3 ) and
is only marginally influenced by shock waves. In this case, where the specific energy deposition is
only 1.66 kJ/g, the Li temperature is predicted to rise by about 600 K, with a (compressional)
pressure of about 900 MPa.
An alternate hydro-dynamical calculation for 5x10 10 238 U ions with 1 A GeV impinging on a 7 cm
thick liquid Li column was performed by A.Tauschwitz et al. [80]. Again, the beam spot was
assumed to have a Gaussian shape with σx = 4 mm and σy = 8 mm. A simple analytical linear
Mie-Grueneisen equation of state was assumed. The particular feature of these calculations is that
reflections of the pressure waves at the free surface of the Li column are taken into account. As a
result, negative (tensile) pressures appear. If this tensile pressure exceeds the tensile strength of
liquid Li at the respective temperature, the jet is predicted to spall; i.e. a free surface develops
within the fluid. Unfortunately, no data are available in the open literature for the tensile strength of
liquid Li. In Ref. [80], a formula given by Grady et al. [81] has been used to estimate a numerical
value for this quantity. The resulting value is only 9 MPa, which would imply that in the scenario
assumed above the jet would break after only 210 ns (Figure 2.4.125). A comparison of the kinetic
energy of the spalled part of the liquid with the work for its detachment indicates that the material
would move outward and break off from the jet.
It is obvious that further experimental and theoretical investigations are needed to make more
reliable predictions for the operation limits of a liquid-Li jet. In particular, it is foreseen to measure
the tensile strength of liquid lithium with the help of a laser Doppler vibrometer in an explosion
chamber at IHED Moscow [82].
Figure 2.4.125: Calculated pressure profile on the axis of a 7cm liquid Li target after the penetration of
5x10 11 1 A GeV 238 U ions within 50 ns, at 210 ns after the beam interaction (according to Ref.[80]). The
assumed Gaussian beam spot has σx = 4 mm and σy = 8 mm. At s = 8 mm from the point of impact of the
beam, a negative pressure develops that exceeds the estimated spall strength of liquid Li of 9 MPa, leading
to a destruction of the target.
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