Atomic Cluster Expansion

The expansion of the nanoplasma is driven by two pressures, the Coulomb pressure arising from repulsion between ions following a charge build-up Qe on the cluster of radius r:

See formula (5) [TD69.pdf, page 313]

and the hydrodynamic pressure from the hot electrons (one can think of the hot electrons expand outwards, dragging the ions with them):

See formula (6) [TD69.pdf, page 313]

where k is the Boltzmann constant and Te the electron temperature. The Q/r4 scaling of PCoul shows that it will be important for small clusters or for low Z clusters where the electrons are not confined and Q can become large. The hydrodynamic pressure scales as r-3 (since ne ~ volume-1), so is therefore more important for larger clusters. The internal pressure driving the cluster apart can be huge. For realistic nanoplasma conditions (ne = 1023 cm-3, kTe = 1 keV), the hydrodynamic pressure, PH ≈ 100 Mbar. It is hardly surprising that the end result is an explosion of the nanoplasma that gives rise to a shrapnel of high energy ions and electrons. The cluster expansion rate is calculated in the model by equating the rate of change of the cluster kinetic energy (proportional to the total pressure PCoul + PH) with the rate at which work is done by the plasma in its expansion [41]. At any stage in the interaction the model allows the relative significance of the Coulomb and hydrodynamic pressures to be compared. Simulations shows that 'PH dominates over PCoul for Ar, Kr and Xe clusters greater than r'' > 2 nm. [TD69.pdf page 313-314]

See Also

3.14 - Vortex Theory of Atomic Motions
5.8.5 - The complete Contraction Expansion Cycle is as follows
9.27 - Expansion and Contraction
13.04 - Atomic Subdivision
16.15 - Negative Electricity is Expansion
Atomic Cluster Heating
Atomic Cluster Ionization
Atomic Cluster X-Ray Emission
Atomic Clusters
Atomic Force
atomic mass
atomic number
atomic theory
atomic triplet
atomic weight
Egyptian fraction expansion
Figure 13.06 - Atomic Subdivision
Figure 14.10 - Proportionate Tonal Relations dictate Contraction or Expansion
Figure 3.28 - Compression and Expansion Forces in Gyroscopic Motions
Figure 9.10 - Phases of a Wave as series of Expansions and Contractions
Figure 9.5 - Phases of a Wave as series of Expansions and Contractions
Formation of Atomic Clusters
Hydrodynamic Equations - Vortex Motions
Hydrodynamic Expansion
Laser Cluster Interactions
Law of Atomic Dissociation
Law of Atomic Pitch
Law of Oscillating Atomic Substances
Law of Pitch of Atomic Oscillation
Law of Variation of Atomic Oscillation by Electricity
Law of Variation of Atomic Oscillation by Sono-thermism
Law of Variation of Atomic Oscillation by Temperature
Law of Variation of Atomic Pitch by Electricity and Magnetism
Law of Variation of Atomic Pitch by Rad-energy
Law of Variation of Atomic Pitch by Temperature
Law of Variation of Pitch of Atomic Oscillation by Pressure
Models of Laser Cluster Interactions

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