1

Plasma physics in Rostock with Gerd Röpke -

from the work in the seventies to new

developments

Humboldt Universität Berlin Institut für Physik

Werner Ebeling Humboldt University Berlin

Content

• I. Quantum statistics in Rostock in the early seventies

• II. Some of the new developments with Gerd Röpke

• III. A special problem: the relations between physical • and chemical picture

• IV. Conclusions

I. QS in Rostock before GR arrived. Plasma group in Rostock 1971

• First row: from r. Sändig, Krienke, Kelbg, guest, Ulbricht, Ebeling, guest,

• the guests: Harold Friedman (USA) and Jan Stecki (Poland)

• 2nd row: from l. Kraeft, Kremp, Kilimann

In the center of interest was the bound state problem for plasmas and electrolytes, the divergence of the partition f. in plasmas

• Coulombic phase transitions in class ionic solutions/plasmas with Grigo/Sändig/Richert,

• Quantum statistics, virial coefficients, atomic partition function, density dependent minimum of ionization, energy levels with Kraeft/Kremp/Kilim.

• <---- the RED BOOK

\vspa

BPLfunction partition atomic )(

1,2,3,4kknown exactly are ),(

...ln)(

)(ln)()()(

2

2

35

2/54

2/53

22

2/31

TC

eTC

nnTC

nTCnnTCnTCnTCnp

k

Exact thermodynamic results:4 virial coeffcients are exactly known

Higher orders=3 part b.s., 4 part b.s.,..

A special problem: First order Coulombic phase transitions in

electrolytes and quantum plasmas • Simplest model of a first order phase

transition is the van der Waals gas,

• A model of similar simplicity exists for a phase transition in Coulomb systems (CPT or PPT) based on Debye-Hückel approximation and Bjerrum-Saha MAL (E./Sändig/Grigo/Fisher/Levin et al.)

Excess chemical potential in Debye-Hueckel approximation

The two-phase region

Specific volume

Quantum Debye-Hückela --> a(T) = Lambda/8

The critical point of the PPT

~12000 - 18000 K

No data for plasmas were available in the 70ties, except Kormer-group (wrong?),Observed transitions in semiconductor

plasmas, metal-amm. ?

• Recently:

• new observations in e-h plasmas,

• new exp for ionic liquids (tetraalkylamm salts - Schröer)

• New exp for high pressure plasmas (Trunin & Fortov groups)

• Now: existence of PPT is rather sure!

II. Quantum statistics in Rostock since 1977 with GR

• GR started his career in Leipzig with Prof. Heber (dissertation on theory of magnetism), then he moved with Heber to Dresden and finally got 1977 a position at U Rostock

• a large influence on Gerd had his russian teacher and friend Dmitri N. Zubarev

• several longer stays Moscow e.g. in 1968, books with Zubarev and Morosov

• later close collaboration with JINR Dubna

Gerd in Rostock since 1977

• He was appointed for theoretical physics at Rostock University at 01.02.1977

• lectures in thermodynamics, quantum theory, statistical physics etc.

• wrote several textbooks e.g. Quantum Theory, Nonequil. Statistics

• In research he joined the group of G. Kelbg and worked with DK, WK, WE and others

........... ..the group

• Günter Kelbg,• Heinz Ulbricht,• Dietrich Kremp,• Wolf-D. Kremp,• Klaus Kilimann,• Hartmut Krienke,• Lutz Schimansky-Geier• Ahlbehrend, Malchow,• Engel-H, Meister

In collaboration with GR new tools were applied and developed, as Green functions, Zubarev formalism, transport theory

• New results are summarized 1986 in the green book

• Quantum theory of density-dependent energy levels, Bethe-Salpeter equation etc. Kilimann/Kraeft/ Kremp/Röpke/Rösler/ Zimmermann

BSE:Closing the gap between H-levels and continuuum (ZKKKR)

The valley of bound states, transition to highly ionized states (Mott transition)

1028

1024

1020

1016

102 104 106

ne, cm-3

T, K

Metallic plasma

Strongly Ionized plasma

mo

lecu

lars

ato

ms

H2 = 0.5

= 0.5

rs = 1

nee3 = 1

= 1

rD = 0.84a0

Phase diagram

Calculations

New results in TD: advanced Pade appr. (Sändig, Zimdahl, Richert, Förster, Kahlbaum).

Example=electronic part of energy:

reasonableea

rea

rea

re

90-..: many calculations for H-plasma (BFJRR)pressure and PPT in Mbar region

Coexistence line /diss. /ioniz.

How to reach the PPT transition line?Hugoniots or (quasi-adiabatic) multishocks?

Transport theory

• D.N. Zubarev, G. Röpke, A.A. Morosov: Statistical mechanics of nonequilibrium processes.

• Wiley, Vol. I 1996, Vol. II 1997

• Few words about him ....

• Go to special problem ....