Leonid E. Zakharov's Web Page

I am a Principal Research Physicist at the Princeton Plasma Physics Laboratory (Room A130). You can reach me at
t.n.  609-243-2630
fax 609-243-2662

Leonid E. Zakharov
Princeton Plasma Physics Laboratory MS27
P.O. Box 451
Princeton, NJ 08543

---Material on this web page is organized in the inverse chronological order---

(the title and the marker .ps are linked to the original .ps file, the marker .pdf is linked to the derived .pdf-file, the markers .ps2, .pdf2 are linked to compact 2viewgraths/per page versions. .ps, .ps2 files can be big)

Lithium: the key to fusion power:

2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999

Numerical codes and theory. 2009

Real Time Forecast (RTF) of tokamak discharges
The theory of Equilibrium reconstruction
Equibrium and associated codes for download:

Year 2013 (-> top)

2013, May 30, Xujing Li: "Introduction to the Edge Equilibrium Code (EEC)" .pdf file.

The talk presents the Edge Equilibrium Code (EEC), which is a new solver of the Grad-Shafranov equation complementing the existing ESC code (based on Fourier representation). EEC, being developed
specifically for the near edge region with an arbitrary shape of the plasma boundary,  uses adaptive flux coordinates with Hermite finite element representation. A special routine for fast solving the sparse matrix equations was created for EEC.

The edge solution of EEC is matched with the core solution from ESC through a  virtual boundary and the two codes communicate as two parallel processes. This approach addresses the future needs in enhancing functionality of EEC without conflicting with the interface of both codes.  The CodeBuilder (Cb), which maintains the documentation and the
source code consistent with each other, was used for the code development.

The resulting ESC-EEC code system acquired unmatched ability (a) in fast free and fixed boundary equilibrium calculations for arbitrary plasma shapes, (b) in using both (r-z) and different flux coordinates, (c) in choosing different
combinations of input profiles, (d) in performing equilibrium reconstruction together with variances analysis, and (e) in assessing the diagnostics used for equilibrium reconstruction, and (f) in high speed of calculations suitable for the Real Time Forecast of tokamak discharges.

2013, May 15, Are "transport barriers" a zone of good confinement or of its collapse .pdf file.

For 3 decades, sharp electron temperature jumps at the plasma edge in H-mode or in ITBs in the plasma core are interpreted as regions with suppressed transport - ``transport barriers''.

The key assumption in this interpretation is the existence of the perfect magnetic surfaces. In fact, for the plasma edge there is no minimal experimental or theory reason for plasma having good magnetic surfaces at the edge. Instead of the widespread but baseless assumption, the relaxing of it leads to the understanding of temperature pedestals, consistent with the  basic experimental data and free of plasma physics miracles, like ``transport barriers''.

Year 2012 (-> top)

2012, December 18, "What Fusion Energy Science (FES) do we have 15 years after TFTR" .pdf file.

In defiance to many "fantastically incorrect statements" of opponents fusion propaganda (which is intended to power the world  from "seawater" while being "unaware of any major project failure in magnetic fusion research") often  uses a trick of making people feel fool in front of  "computer simulations of plasma turbulence which helps scientists predict plasma behavior"

In fact, these simulations and the three decade long obsession of FES with the core transport, were critical in termination progress in fusion. During the last 15 years the fusion program followed  exactly the path understood and predicted by "The theory of the failure  of magnetic fusion" (LZ, 2004), i.e., from progress to stagnation, and then to degradation, when science no longer plays a role.

At this point the result is devastating. After 3-4 decades of development:
The energy "vision" of FES (except its energy from "seawater") is simply ridiculous. After 15 years of existence, FES failed not only in the energy aspects, but even in of science. The situation with FES can only get worse.

In contrast, the basic level of science of magnetic fusion has been created in a separate, essentially underground effort. It
provided a much deeper understanding of the tokamak plasma and now raises the necessity of a separate program which would aim toward a PDT=100-200 MW DEMO device with the electric Q factor exceeding unity. 

August 17, "LiWall Fusion - no alternative, no other option" .pdf file.

This is a white paper prepared for FESAC discussion on the near-term fusture of the magnetic fusion energy program. The paper displays the depth of fundamental problems of MFE, which cannot be solved by the presently adopted approach to fusion. In parallel to the deep stagnation of the progress of fusion, the scientific level of the research is deteriorating at fast speed. In a sharp contrast to the conventional fusion, the LiWall Fision (LiWF) concept opens the way of resolving issues of confinement, stability, power extraction, etc, thus, leading to a practical approach to fusion energy.

In particular, LiWF formulates the specific burning plasma (BP) regime and a concept of DEMO, which in the current program remain only at the propaganda, rather than physics, level.

Year 2011 (-> top)

2011, September 21, "Scalable Flowing Liquid Lithium (FLiLi) system" .pdf file   27.6 MB movie Alcohol/Copper Prototype of FLiLi, fabricated by the author.

A practical system for implementation of a flowing plasma pumping liquid lithium layer (FLiLi) in tokamaks is proposed. The suggested scheme suggests a unique approach for power extraction from tokamaks, which combines a new high performance regime (called LiWall Fusion regime and associated with efficient pumping of plasma particle by flowing lithium) with a heat sink (actively
cooled by He gas with expected power extraction rate of  10 - 15 MW/m2 at relatively low gas temperature  300o C).

The FLiLi system conceptually resolves the issue of maintaining the plasma facing lithium surface clean and insensitive to the in-vessel tokamak environment.

Year 2009 (-> top)

2009, April 24,  -KSTAR Seminar,   National Fusion  Research Institute, Daejeon, Korea.  "The basics of the LiWall Fusion (LiWF) concept" .pdf file and compact  .pdf2 file.

The presently adopted plasma physics concept of magnetic fusion has been originated from the idea of providing low plasma edge temperature as a condition for plasma-material interaction. During 30-years of its existence this concept has shown to be not only incapable of  addressing practical reactor development needs, but also to be in conflict with fundamental science of a stationary and stable plasma.

Meanwhile, the demonstration of exceptional pumping capabilities of lithium surfaces on T-11M (1998), discovery of the quiescent H-mode regime on DIII-D (2000), and a 4 fold enhancement of the energy confinement time in CDX-U tokamak with lithium (2005), contributed to a new vision of fusion relying on high edge plasma temperature. The new concept, called LiWalls, provides a scientific basis for developing controlled fusion as a component of the nuclear energy or a fusion power reactor.

The talk gives an introduction to the LiWF concept for KSTAR people.

2009, March 17, Renew Workshop Theme 5 - Optimizing the Magnetic configuration, PPPL, Princeton NJ.  White  paper "ST1, EAST1, ITER-100 - all exceeding ignition criterion",  and viewgrapths of the talk as .pdf file and compact  .pdf2 file.

White paper summarizes 10 years of LiWF concept, which essentially has resolved the plasma physics puzzle of magnetic fusion.

The talk explains the crucial role of plasma boundary for energy confinement. This understanding makes the LiWF regime insensitive to existing unknowns in transports properties of the plasma core and essentially nullifies the value of core transport studies. The appropriate experiments on NSTX (if modified into ST0 facility for LiWF regime studies) can quantify the role of trapped electron modes and secondary electron emission and give the necessary data for designing the next step spherical tokamak (ST1) for PPPL (capable of demonstrating DT ignition relevant plasma parameters using DD plasma), the stationary tokamak EAST1 (for fission-fusion studies), and a regime with 100 MW of DT equivalent fusion power at early (hydrogen) phase of ITER.

2009, January 22, PPPL Experimental Seminar, Princeton NJ, "How far is magnetic fusion from being a component of nuclear energy" .pdf file,  and compact  .pdf2 file.

Without abandoning its noble goal for clean inexhaustible energy source based on fusion of hydrogen isotopes, fusion can much more realistically achieve an intermediate, but not less important, goal to be a component of re-emerging nuclear energy industry. Instead of producing energy from its 14 MeV neutrons, it can better utilize them for converting U-238 or Th-232 into fissile elements for the first load of the fast breeder reactors (or to a reasonable portion of fuel) in order to close the fuel cycle of conventional nuclear reactors.

Three huge problems, i.e., (a) tritium breeding in unprecedented amounts, (b) destruction of the First Wall by 14 MeV neutrons, and (c) extraction of  high-temperature (700-800$^o$ C) heat from the nuclear zone of a toroidal device, which are still behind the horizon of "clean" fusion and never been touched, are dramatically mitigated to near non-existence in the role of fusion as a fuel preparation component of  nuclear energy.

Even this "truncated" fusion-fission (FF) mission cannot be accomplished based on the present "main stream" approach, which as plasma physics research is getting more and more fragmented, and is trapped into its hopeless 35 year old concept of a fusion power reactor.

Instead, this talk outlines the theoretical and experimental basis of the LiWall Fusion (LiWF) concept, which was first presented to PPPL 10 years ago and which is based on new plasma regimes, i.e., "core fueling by neutral beam injection & pumping plasma edge by a lithium surface". By eliminating the dependence of confinement on anomalous electron transport, edge localized modes,  peaking of the plasma current, thermo-force (driving  impurities to the plasma), needs for alpha-particle heating, etc, LiWF is very well suitable for the FF mission, suggesting realistic devices with a JET-size plasma for demonstration of the FF mission.

Year 2008 (-> top)

2008, August 25-26, Resonanant Magnetic Perturbation Modeling Workshop, General Atomic, San Diego, CA, "Where is the edge in toroidal plasmas ?" .pdf file,  and compact  .pdf2 file.

It is believed that by definition the plasma edge is the separatrix which separates the confinement zone from the convection dominated plasma periphery. Another belief is that the H-mode has a miraculous "edge transport barrier" providing a steep temperature pedestal in front of the last closed magnetic surface. 

The DIII-D experiments with Resonant Magnetic Perturbations undermine both of these beliefs. Instead, the interpretation of these experiments suggests that the top of the edge electron temperature pedestal, rather than the separatrix, represents  the  end of  the electron energy confinement zone, i.e. the edge for the electron temperature.  On the other hand, the  edge for the  ion temperature and plasma density seems to be situated at the separatrix (or behind it).

The same experiments suggest the existence of intrinsic MHD perturbations near the separatrix (probably related to the Scrape Off Layer Currents measured on DIII-D by H.~Takahashi) which determine the finite width of the electron temperature pedestal.

2008, Three talks at Chinese Academy of Science, Institute of Plasma Physics, Hefei, Anhui Province, China:
1. July 07, 2
008, "The LiWall Fusion (LiWF) Concept (part I)" .pdf file,  and compact  .pdf2 file.
2. July 09, 2008, "LiWF  & Spherical Tokamaks (part II)" .pdf file,  and compact  .pdf2 file.
3. July 14, 2008, "Three Step Program toward the Reactor  Development Facility (RDF, part III)" .pdf file,  and compact  .pdf2 file.

All critical aspects as well as existing theoretical and experimental data which support  the new approach to magnetic fusion are outlined in three talks in as systematic manner.

2008, April 15 Experimental Seminar, PPPL, Princeton NJ, 2008,  March 26, 21st Transport Task Force (Boulder CO), "Where  is the  edge  in toroidal plasmas" .pdf file,  and compact  .pdf2 file.
It is believed that by definition the plasma edge is the separatrix which separates the confinement zone from the convection dominated plasma periphery. Another belief is that the H-mode has a miraculous "edge transport barrier" providing a steep temperature pedestal in front of the last closed magnetic surface.

DIII-D experiments with Resonant Magnetic Perturbations undermine both  of these beliefs. In addition, the recent discovery of the instability of the so-called Wall Touching Kink Modes (and their edge version, the Takahashi Kink Modes) gives a basis for an emerging self-consistent understanding of the plasma edge and its MHD activity.

008,  March 24, Physics Seminar at University of Wisconsin (Madison WI), March 25University of Illinois Urbana  (Champaign IL), "LiWall Fusion and its 3 step R&D program toward a Reactor Development Facility" .pdf file,  and compact  .pdf2 file.

2008,  January 10, Theory Meeting, PPPL, Princeton NJ, "The kink mode during the disruptions" .pdf file  and compact  .pdf2 file.
The talk explains the locked m/n=1/1 kink mode during the vertical disruption event when the plasma has an electrical contact with the plasma facing conducting surfaces. It is shown that the kink perturbation can be in equilibrium state even with a stable safety factor q > 1, if the halo currents, excited by the kink mode, can flow through the conducting structure. This suggests a new explanation of the toroidal asymmetry in magnetic measurements and so-called sideway forces on the in-vessel components during the disruption event.

In addition, the talk confirms the fundamental role of the halo currents (named here as "Hiro" currents), which interaction with the free boundary kink modes was in many occasions emphasized earlier by Hiro Takahashi and Eric Fredrickson. In fact, the physics of Hiro currents can explain four edge plasma stability regimes in tokamaks in a way consistent with DIII-D experiments.

Year 2007 (-> top)

2007,  November 16
, APS-2007 Meeting (Rosen Center Hotel, Orlando FL), "The theory of the failure of magnetic fusion" .ps file.pdf file and compact  .ps2 file.pdf2 file.
In the physics of the 20th century, fusion represents an extraordinary  failure which eroded expectations of society on an ``unexhaustible'' energy source. The question is if these 50 years of research did really prove that fusion will be forever a "carrot'' on a stick and always 35 years from its implementation.

When a person is asking fusion people why this program is full of  broken promises, he (besides conventional complaints on the lack of funding) is typically getting the answer that the problem itself is the most difficult one that physics ever faced. In the FSU, such characterizations were done as early as in the 60s by Lev Artsimovich, the leader in the field.

This view is only partially applicable in the 21st century. Since the Artsimovich time, fusion, as a "difficult'' problem, has been converted into the "complicated'' one (around the late 80s). The presented theory makes a clear distinction between these two kinds of problems, which require significantly different management approaches, and explains the current stagnation in magnetic fusion by the lack of understanding this crucial  difference.

The "difficult'' problem self-organizes its own solution and does not require intervention of management. The state of the "difficult''  problem is improving with time.

If an unresolvable issue was encountered, the "difficult'' problem is converted into a "complicated''  one. Without external intervention, the "thermal death'' state of the "complicated''  problem is getting only worse with time.

There is no natural way back from the "complicated'' phase. Only an external "brute'' force with "low entropy'' means (computers, money, and sufficient intellect to make the problem "difficult''  again) can reverse the situation.

Accordingly, it is not possible to expect that, without changing the management approach (or starting a new program), the hopelessly fragmented magnetic
fusion would be capable to deliver the promised energy source.  

  2007,  October 24-30, Fusion Energy Seminars in LANL (Los Alamos NM), GA (San Diego CA), UCLA (Los Angeles CA), LLNL (Levermore CA), "LiWall Fusion and its 3 step R&D program toward a Reactor Development Facility" .ps file.pdf file and compact  .ps2 file.pdf2 file.
The talks in several fusion Labs were a response to the Orbach/Bodman initiative for domestic fusion. In particular, the proposed program includes short term experiments on plasma pumping with a lithium loaded plate on NSTX and conversion of this machine into a spherical tokamak ST0 with a mission to demonstrate the feasibility of the LiWall regime with 2-3 times better confinement than at present on NSTX.

2007,  August 07, FESAC Strategic Planning Panel meeting, PPPL Princeton NJ, "LiWall Fusion and its 3 step R&D program" (2 slide presentation) .ps file.pdf file and  White paper .ps file.pdf file,

The presentation was made as a response to the FESAC charge by the Director of the DoE Office of Science R. Orgach on domestic fusion program beyond the ITER. The essence  of the LiWall Fusion (LiWF) concept was explained in a compact form together with its R&D program targeting development of the Reactor Development Facility. Early this absolutely necessary step in developing a practical fusion was known as a neutron source but then abandoned because of incapability of magnetic fusion to meet the RDF's requirements. Now, with LiWF concept completed, the RDF seems to be within present plasma physics and technology. In contrast to LiWF, the presently dominant concept of fusion, referred as the BBBL-70s ("The Bibble of the 70s"), with its "road map" and "burning plasma" projections, appears to be irrational and non-scientific in all crucial issues of fusion as a possible energy source. 

2007,  April 11, PPPL Colloquium, PPPL Princeton NJ, "3-step program toward a Reactor Development Facility", .ps2 file  .pdf file .pdf2 file.

The presently adopted plasma physics concept of magnetic fusion has  originated from the idea of providing low plasma edge temperature  as a condition for plasma-material interaction. During 30-years of  its existence this concept has shown to be not only incapable of  addressing practical reactor development needs, but also to be in  conflict with fundamental aspects of stationary and stable plasma.

Meanwhile, a demonstration of exceptional pumping capabilities of  lithium surfaces on T-11M (1998), discovery of the quiescent H-mode  regime on D-IIID (2000), and a 4 time enhancement of the energy  confinement time in CDX-U tokamak with lithium (2005), contributed  to a new vision of fusion relying on high edge plasma temperature.  The new concept, called LiWalls, provides a scientific basis for  developing magnetic fusion.

The talk outlines 3 basics steps toward the Reactor Development  Facility (RDF) with DT fusion power of 0.3-0.5 GW and a plasma  volume ~30 m^3. Such an RDF can accomplish three reactor objectives  of magnetic fusion, i.e., (a) high power density ~10 MW/m^3 plasma  regime, (b) self-sufficient tritium cycle, (c) neutron fluence  ~10-15 MW⋅ year/m^2, all necessary for designing the DT power  reactor. Within the same mission a better assessment of DD fuel for  fusion reactors could also be possible.

The suggested program includes a series of 3 spherical tokamaks.  Two of them, ST1, ST2, are DD-machines, while the third one, ST3,  is the RDF itself with a DT plasma and neutron production.

All three devices rely on a NBI maintained plasma regime with  absorbing wall boundary conditions provided by the Li based plasma  facing components. The goal is to utilize the possibility of high  edge temperature plasma with the super-critical ignition (SGI)  regime, when the energy confinement significantly exceeds the level  necessary for ignition by a-particles.

Specifically, the mission of ST1, with a size slightly larger than  NSTX in PPPL but with a four times larger toroidal field, is to  achieve the absorbing wall regime with confinement close to neo- classical. In particular, the fusion factor QDT-equiv~5  corresponding to conventional ignition criterion has to be achieve.

The mission of ST2, which is a full scale DD-prototype of the RDF,  is the development of all other plasma physics aspects of  stationary regime with QDT-equiv~40-50.

ST3 is the DT device with QDT~40-50 with sufficient neutron  production to design the nuclear component of a power reactor.  Still the mission of ST3 contains a significant plasma physics  component of developing a-particle power and He ash extraction.

As a motivational step (ST0), the suggested program, assumes a  conversion of the existing NSTX device into a spherical tokamak  with lithium plasma facing components. The demonstration of  complete depletion of the plasma discharge by lithium surface  pumping, first shown on T-11M, can be considered as a well-defined  criterion of readiness of the machine for the new plasma regime.  The final mission of ST0 would be doubling or tripling the energy  confinement time with respect to the current NSTX.

  Year 2006 (-> top)

2006,  December 11, NSTX Physics Meeting, PPPL, Princeton NJ, "Lithium and NSTX".pdf file .pdf2 file. Necessity of new plasma regimes on NSTX  is emphasized and a specific approach using a Li loaded plate as an option for Li based plasma facing component on NSTX  is presented as a turning point of  its program toward fusion development.

2006,  November 02, Invited talk to APS 2006, Philadelphia PA, "Ignited Spherical Tokamaks as a Reactor Development Facility", .ps2 file  .pdf file .pdf2 file.  The Lithium Wall Fusion (LiWF) concept, now completed, is presented and compared with the "Mainstream" Magnetic Fusion (MMF) approach. While LiWF is self-consistent and relies on existing technology and the present understanding of fusion,  MMF is in conflict with the science recommendations regarding all critical issues of the reactor. Necessity of a separate, reactor development program (~$2-2.5B for ~15 years), is  emphasized.

2006,  July 21
, UKAEA Fusion Theory Colloquium, UK,  "Getting serious about Fusion", .ps2 file  .pdf file .pdf2 file. This provocatively titled talk presents an unconventional view on the basic issues of magnetic fusion (excluding its nuclear issues), such as: core fueling, confinement, stability, power and He extraction from the plasma.  A super-critical regime is  suggested  when alpha heating is not essential for sustained  fusion power production. An unusual similarity between Spherical Tokamaks and stellarators is also mentioned.

A separate national program (about $2-2.5 B for 15 years), if launched, can realistically develop an Ignited  Spherical Tokamak (IST) as a fusion neutron source for reactor R&D in 3 steps (2xDD, 1xDT), i.e.:

1. A spherical tokamak, targeting achievement of the absorbing wall regime with neo-classical confinement in a DD plasma and  Q_{DT-equiv}=1,
2. Full scale DD-prototype of IST for demonstration of all aspects of a stationary super-critical regime with Q_{DT-equiv}=50.
3. IST itself with a DT plasma for reactor R&D and alpha-particle power extraction studies with Q_{DT}=50.

While being focused on the Reactor Development Device (IST), the approach is consistent with the smooth transition to the power production phase relying on stellarators, as the power reactors, optimized for the super-critical ignition regime.

2006,  January 25, PPPL Research Seminar,  "Thermodynamics, science and religion in fusion", .ps2 file .pdf2 file The talk represents an extended version of sections 3-5 of the  Jan.11 talk. It explains a unique role of the Spherical Tokamaks for developing a fusion power reactor. Also the analysis of the situation in the fusion program (sent  earlier to OSTP) is presented. It explains why, in the absence of scientific leaders, such a complicated scientific program, as fusion, unavoidably becomes fragmented and fells into an "activity trap". Instead of being exposed, the real problems of fusion are put under the rug, the calibration to the final goal is avoided and replaced by a propaganda, and the otherwise good science in the field fails to produce progress toward the power reactor. Being thermodynamically equivalent to a thermostatic, "thermal death" situation, the present state of fusion program is essentially irreversible. In order to utilized the accumulated intellectual, scientific and technical potential of fusion it is much more efficient to initiate a separate program, targeting Ignited Spherical Tokamaks for development of the power reactor, than trying to reverse natural tendencies or fix the current over aged program.

2006,  January 11, PPPL Research Seminar,  "Ignited Spherical Tokamaks for developing a power reactor", .ps file .pdf file The talk reports the completion of the LiWall concept and provides argumentation for necessity of a special fusion reactor development program based on ISTs.

Year 2005 (-> top)

2005,  October 27, JET Task Force D Meeting,  "Calibrating JET for equilibrium reconstruction", .ps file .pdf file The calibration technique for JET tokamak is presented. It targets elimination of uncertainties in magnetic signals due to the presence of the iron core and due to eddy currents in passive conductors.  The correlation matrix between sensors located outside and inside the vacuum vessel is introduced in order to determine the parasitic n != 0 perturbation in magnetic fields generated by the iron core. The time dependent matrix of response functions is introduced in order to eliminate the n != 0 perturbation generated by the eddy currents. While both elements can be determined using only the calibration shots (without the plasma), they allow to pre-process magnetic signals of plasma discharges for further use in the equilibrium reconstruction codes.  The calibration technique is planned to be implemented on JET using the existing experience with the similar approach developed for CDX-U tokamaks and with numerical code Cbc2e.

2005,  October 10
, Int. Workshop on Exp. Performance of KTM Tokamak, Astana, Kazakhstan,  Oct. 10-12, 2005" Ignited Spherical Tokamaks for development of power reactor(.ps2 file, .ps file .pdf file) After 6.5 years since its first formulation the LiWall approach for tokamak fusion has demonstrated its conceptual consistency for both reactor development and for low-activated reactor itself. While the currently dominant tokamak approach is locked into the single concept of divertor based power extraction, particle control and He pumping, which is incapable to resolve any of fundamental magnetic fusion issues even at the plasma physics level, the utilizing the Li Wall  properties opens the way of resolving the energy confinement, plasma stability, power extraction, and Helium exhaust problems in a manner consistent with the power reactor physics. Instead of useless for reactor development philosophy of "burning plasma", externally driven "component test facility", the approach results in Ignited Spherical Tokamaks, capable of high fusion power density regime for developing the first wall and the tritium cycle of the future power reactors.

2005,  August 11, Unanswered (too negligible) old message to OSTP, Nov. 2, 2004"ITER, fusion and the power reactor(.pdf file). The reason of stagnation of the current magnetic fusion program (more than 35 years old) is identified as a lost of the leadership structure in the middle of 1980s when magnetic fusion felt short in providing a tokamak design concept capable of 10-15 MW.year/m^2 in fluence of neutrons, necessary for development of the reactor components. Then, the conceptual problem was hidden under the rug, while the subsequent fragmentation of the research resulted in the "thermal death" situation, when the fusion program became entrapped into details of outdated fusion concepts, at the same time, blocking the new developments.

The necessity of a separate (from the current FES) reactor development program for the US is emphasized. (See, also Oct. 2004, Fusion Eng. and Design.)

2005, July 19. Simposium on Integrated Modeling
"At the ground level of  integrated modeling" (.pdf file).  For any numerical code the number of possible runs can be apprehended only if expressed at the logarithmic scale in the form of entropy. What really limits the entropy is the intellect of the author and his understanding of the problem rather than "if()" statements inside the code. The computer languages, perfect in handling the  "if()"-like statements, do not provide the adequate mechanism for expressing the author's understanding, thus, leaving the entropy of the code unlimited for the unexperienced user. The problem could be addressed only if the very basic level of integration is formalized in an "entropy-free" manner using the computer ("entropy-free") power for its implementation.

The talk discusses the most rudimentary level of integrated modeling, level which cannot be avoided or substituted by the sporadic patching the loopholes with OOP, FWEB, etc. In 1996 this understanding resulted in the CodeBuilder (Cb) idea which became functional in 1997. It  provides a formalized mechanism for mutual mapping of "people's minds" and virtual structures inside the codes, associated sources, data, documents, etc.  While being created earlier than XML (based on somewhat  similar ideas), Cb represents a more fundamental approach for resolving the problems of integrated modelling. The talk is illustrated with examples of Cb generated codes (Cbesc, Cbbst) and their integration with others (ASTRA).

Oct. 2004, Fusion Eng. and Design.  72 (2004) 149-168
"Ignited Spherical Tokamaks and Plasma Regimes with LiWalls" (.pdf file) Basic requirements of the fusion power reactor and its development are outlined. The notion of Operational Power Reactor Regime (OPRR) is introduced explicitly for the first time in order to distinguish it from the relatively short ignition phase of the reactor operation. Development of OPRR is intrinsically linked to two basic technology objectives, i.e., development of the First Wall (FW) and the Tritium Cycle (TC). The paper reveals an existing fundamental gap in the reactor development path associated with the lack of necessary amounts of tritium for the reactor design development. In this regard, low recycling regimes with a plasma limited  by a lithium wall surface suggest enhanced stability and energy  confinement, both necessary for tokamak power reactors. These regimes also could make ignition and OPRR feasible in compact tokamaks. Ignited Spherical Tokamaks (IST), self-sufficient in the bootstrap current, are introduced as a necessary interim step for development OPRR-FW-TC for the power reactors.

Tokamaks with Lithium covered walls. Year 2004 (-> top)

2004,  January 20,27  "Ignited Spherical Tokamaks and their place in fusion"  (.ps file, .pdf file)  Presented to Fusion Theory Colloquia, UKAEA and to JET EFDA Seminar, Culham, UK.
Three basic aspects of the reactor physics and technology, i.e., Operational Power Reactor Regime (OPRR), development of the First Wall (FW), and of self-sustained Tritium Cycle (TC) are discussed in the talk. 

The notion of OPRR is introduced explicitly in order to distinguish it from the relatively short ignition phase of the reactor operation. In contrast to ignition, OPRR requires new confinement and stability regimes with high beta (>8 %) and relatively small confinement time (<1.5 sec). Being a challenge for the plasma physics, OPRR cannot be developed without use of the fusion power. At the same time, the physics and technology of FW and TC cannot be developed without OPRR.

Such a generic link between 3 key elements of the reactor physics together with consumption of large amount of tritium for their development, creates a gap on the development path toward the magnetic fusion reactor.

In this regard, Ignited Spherical Tokamaks (IST) seem to be the only feasible concept for bridging the gap between the present physics and future power reactors. The expected green light for the ITER puts development of IST (from the very basic level) into the agenda as a necessary and complimentary to ITER fusion reactor R&D program.

Tokamaks with Lithium covered walls. Year 2003 (-> top)

2003,  April 10  "Low recycling ITER operational regime, its fueling, pumping and He control"  (.ps file, .pdf file)  Presented to APEX/ALPS Meeting, Grand Canion, AZ .A recent theory of island held equilibria in tokamaks explains existence of a slow evolution phase in the tokamak core even when the plasma is "ideally unstable" with respect to m/n=1/1 internal kink mode. Consistent with TFTR data, this theory predicts unavoidable major disruptions in the reference high performance regimes of ITER and, thus, requires their considerable revision. As a result, ITER tentantively should implement the low recycling plasma regime, which would not only eliminate the danger of internal disruptions but would significantly enhance the ITER performance and lead to its ignition. The Diamagnetic "Hot Dog" (DHD) mechanism for refueling and controlling the low-recycling high edge temperature ITER operational regime is aoutlined. This mechanism provides control of fusion power deposition, density and pressure profiles as well as the helium ash exhaust froma the plasma.  The DHD pumping (inverse to fueling) provides transport of hot edge plasma particles to Li coated wall panels (suggested in this regard for ITER wall design), thus making divertor consistent with the high plasma edge temperature. At the same time, the DHD pumping directs the He ions into the divertor for their pumping, thus, suggesting entirely new ITER divertor functionality.

2003,  April 03  "Tokamak reactors, their strategy, operational regime, fueling and control"  (.ps file, .pdf file)  Presented to PPPL Theory  Seminar . The talk outlines objectives and ten basic rules of magnetic fusion strategy. The low recycling Ignited Spherical Tokamaks (IST) are specified as the magnetic fusion devices capable of developing the Operational Power Reactor Regime (OPRR), First Wall (FW) and the Tritium Cycle (TC). At present, only ISTs are consistent with the reactor relevant high-betas, stationary regime (maintained by the bootstrap current and by LiWall pumping), high fusion power density and neutron flux. The Diamagnetic "Hot Dog" (DHD) mechanism for refueling and controlling the low-recycling, high edge temperature OPRR is outlined. DHD fueling is consistent with controlling fusion power deposition,density and pressure profiles as well as with helium ash exhaust from the plasma of power reactors.  The theory of DHD controlled LiWall IST essentially concludes the plasma physics concept of tokamak based DT magnetic fusion and emphasizes the growing role of fusion technology. After 4 years the LiWall-DHD development became a practical theory, requiring technology and experimental implementation.
2003,  March 21  "Negative central current and q_0 < 1 equilibria in tokamaks" (.ps file, .pdf file)  Submitted to Phys.Rev.Lett. A solution for toroidal equilibria is given for the situation with a negative current (j(0) < 0) in the center of the plasma column (with a positive overall current). It includes (a) a central core region with simply nested magnetic surfaces nd a negative total current, (b) an m=1, n=0 magnetic island with a positive current density, and (c) an outer region with the conventional magnetic surfaces and positive  current density. The same solution, applied for q(0) < 1 in tokamaks explains the existence of a stationary phase between internal relaxations in tokamaks with both central pressure  below and  above the ideal Bussac limit. The theory gives a  classification of relaxation  regimes in tokamaks (consistent with observations).
2003,  March 14  "Operational Power Reactor Regime and Ignited Spherical Tokamaks" (.ps file, .pdf file)  Presented to Spring 2003 Plasma Science and Fusion Center Seminar at MIT.  While recently submitted to DoE Really Great 35 year Development Plan (RG35DP) suggests a new, 2003 version of the  magnetic  "cold fusion  without ignition" for the next 35 years, the talk was focused on achieving ignition in tokamaks in the nearest future. It was shown that the Operational Power Reactor Regime (OPRR) requires a wall-stabilized and low recycling plasma.  Because of the small size and  high beta , spherical tokamaks are uniquely suitable for development of  OPRR. It was shown that in the low recycling regime, spherical tokamaks not only are capable for OPRR relevant high-beta, but also are overdriven with the bootstrap current,  calculated now for the first time using direct Monte Carlo particle orbit simulations with the pitch angle scattering.  The Diamagnetic "Hot Dog" (DHD) mechanism for refueling high-temperature low recycling plasma has been reported for the first time. DHD fueling has all properties for providing  full control  of the fusion power deposition, density and pressure profiles in the low recycling tokamak power reactors. The theory of DHD controled LiWall IST essentially concludes the plasma physics concept of the tokamak based DT magnetic fusion and now requires a phase of its focused experimental and technology development, contrary to the eclectic RG35DP "configuration optimization".

2003, February 12  "OPRR, ignited CTF  and Lithium Tokamak Experiment" (.ps file, .pdf file)  Presented to LTX Meeting at DoE Office of Fusion Energy Sciences. The Operational Power Reactor Regime (OPRR) (which is distinct from the Ignition phase) is introduced as a major challenge for magnetic fusion. The necessity for a low recycling regime and a wall-stabilized plasma for OPRR is emphasized. For development of the OPRR, Spherical Tokamaks (ST) are uniquely  positioned as high-$\gb$ small volume devices with good plasma confinement and stability. It is shown that LiWall ST devices with a low-recyling plasma and wall stabilization have the opportunity for ignited operation in a self-sustained magnetic configuration driven by the bootstrap current. The use of the ST in developing the OPRR would provide a new vision for a Component Test Facility (CTF) as a compact (30 m^3) ignited ST (0.5 GW of fusion power) with high (5-8 MW/m^2) neutron wall load and maximum (up to 95 %) use of fusion neutrons for tritium breeding. A compact Lithium Tokamak Experiment (LTX) is being proposed to address the basic plasma physics and technology issues of the low recycling regime, controlled by a lithium wall surface.
2003, January 06  "Magnetic DEMO, CTF fusion reactors and their strategy" (.ps file,  .pdf file)  Presented to NSTX Physics Seminar, PPPL, Princeton, NJ. The basic strategy for development of the DEMO magnetic fusion reactor is outlined. The strategy distinguishes the Operational Power Reactor Regime (OPRR) and the ignition phase. It emphasizes the unique role of Spherical Tokamaks with low recycling, high temperature plasma edge in developing OPRR. The strategy envisions 3 stages for plasma physics and technology development: (a) DD phase with an objective of development of quasy-stationary (bootstrap current driven) high-beta ST regime; (b) Component Test Facility (CTF) phase based on ignited ST  with  objectives of development of the power extraction schemes (from both plasma and the neutron zone) and of a self-sufficient tritium cycle; (c) DEMO electricity production phase, based  on conventional aspect ratio tokamaks with Li/FLiBe based first wall, full shielding and high-temperature FLiBe coolant and a  self-sufficient tritium cycle with an objective of demonstration consistency of the magnetic fusion  with the safety and economics of the power reactor.

Tokamaks with Lithium covered walls. Year 2002 (-> top)

2002, October 30  "Dynamically balanced first wall for the LiWall tokamak-reactor" (.ps file, .pdf file)  Presented to 5th US-Japan Workshop on Fusion High Power Density Devices and Design, UCLA, Los Angeles, CA. The shape of the dynamically balanced first wall has been calculated. The wall structure includes: a) ~1 cm thick intense plasma facing lithium streams driven by magnetic propulsion, b) ~1 mm thick patchy separation guide wall, c) Be wire ropes balancing the
structure (total maximum thickness of the set ~1 cm), d) ~1 mm patchy second separation layer, and e) ~ 10-15 cm
thick Zinkle-Nelson FLiBe blanket. While the existing design approaches to the reactor essentially mimic the large plasma experiments and fail to satisfy all basic requirements of the reactor physics and cost, the presented first wall structure is the first conceptual design which is consistent with the high neutron flux, efficient power extraction as well as with high performance plasma regimes.

2002, March 08  "Magnetic propulsion of Intense Lithium Streams in a Tokamak Magnetic Field" (.ps file,   .pdf file)  Submitted to Phys. Rev.Letters. The theory of magentic propulsion (developed in Dec. 1998) is presented for publication.

2002, Feb. 18. Snowmass 2002 Comments "Li Walls and betatau of the fusion reactor strategy".  The basic principles of magnetic fusion reactor strategy are outlined for further discussion (http://web.gat.com/snowmass/working/ci/c2)

2002, Feb. 11,  CEA Cadarache, France , "Tokamak and tokamak  reactors with Li Walls" - (link to .ps and to .pdf files).  The LiWall concept has been presented in conjunction with Tore Supra program on plasma-wall interaction. A section with the Frequently Asked Questions has been added to the file.

2002, Feb. 07,  EFDA-JET Seminar, Abingdon UK, "Tokamak and tokamak  reactors with Li Walls" - (link to .ps and to .pdf files).  It was shown that the magnetic fusion has no path without a substantial raise in  beta.  While dominant concept in magnetic fusion is full of contradictions, the LiWalls are consistent with basic reactor requirements. Being in all plasma physics aspects more advanced than the conventional fusion, LiWalls it is the only concept making clean  magnetic fusion realistic.

Tokamaks with Lithium covered walls. Year 2001 (-> top)

2001, Feb. 26,  Seminar of Dept. of Nuclear Engineering, MIT , "Yacht-sail approach for the tokamak fusion reactors" - (link to .ps and to .pdf files). Dynamically balanced design concept for the "first wall" of the tokamak fusion reactor has been presented to MIT students. The concept opens opportunities for creativity of nuclear engineers and technologists  in developing acceptable and controllable tokamak fusion reactor.

2001, Feb. 21. Sergei Mirnov Talk at PPPL Experiment Seminar, "Experiments on Tokamak T-11M with a Lithium Capillary-Pore Limiter" - link to the PowerPoint .ppt file. Same viewgraphs (although without comments) in JPEG format  (e.g.,Mirnov01.jpg)  can be accessed at http://w3.pppl.gov/~zakharov/Mirnov010221.

2001, Jan. 29, "Stabilization of tokamak plasma by lithium streams" - .ps file with submission to Comments on Plasma Phys. and Controlled Fusion. A pure academic manuscript, which describes a mechanism of MHD stabilization by Intense Lithium Streams at the plasma edge, discovered together with the LiWall concept in Dec. 1998. Was motivated for publication in summer of 1999 by  a misrepresentation of the LiWalls at the Sherwood-1999 Theory meeting at Los Angeles. Manuscript wasted more than a half year in PRL. Slightly different from the PPPL-3483 report.

2001, Jan. 26, OFES of DoE, "Tokamaks with LiWalls as a concept for fusion reactor" (.ps file, identical to UMD, but presented with a different emphasis).

2001, Jan. 25,  Theory seminar of Institute for Plasma Research, University of Maryland, "Tokamaks with LiWalls: what is interesting about them" (.ps file, slightly different from the PU Ph. Dept. talk on Dec.07, 2000, i.e., without Cbpu code involved).

2001, Jan. 18, Theory seminar at PPPL, "TFTR, DIII-D, and non-recycling regime in tokamaks" - (.ps file with a little bit of what plasma physicists and students should know about low recycling  regimes in tokamaks.)

Outline of this 90 min talk:
I. Research results in physics.
a) TFTR (link to .ppt file of D.Mansfield),
b)T-11M lithium results (link does not yet exist),
c) DIII-D QDBH (.pdf link to a copy of K.Burrell, GA, presentation to APS-2000),
d) Non-recyling LiWall (1998) (.ps link to my PU talk, see pp.14-16), and
c) Sakharov's (1951)

II. Does the tokamak fusion has a path ?
a)  Yes.
b) Consistency between DoE  /   Congress approach to fusion. (link to a US gov. WW2 history document / Views of a Republican Congressman, who can be credited for the shock therapy for the tokamak fusion) .
c) Competence in research and
d) Freedom of communications as a key for securuty of our progress in fusion.
e) Safety of future reactors (any kind of covering up the present reality
from students is 100 \% guarantees of future failures with the fusion reactors) .
III. Yes, it has it and soon it will be on the way.

2001, Jan. 12., PS&T seminar at PPPL, "Power extraction from tokamaks and tokamak-reactors" - (link to .ps file).

Abstract, as it was announced to PPPL Staff.  (Another version, intentionally falsified by the current PPPL management, has been put on PPPL weekly highlights  http://www.pppl.gov/hypermail/PPPL_Highlights/0172.html .)
   Only two aspests of the LiWall concept will be discussed in
presentation :

(a) power extraction from the plasma facing components in tokamaks and
(b) power extraction from the energy absorption layer in the neutron
    zone of the tokamak-reactor, which includes the  a new "Yacht sail"
    approach for the tokamak-reactor design,

(other issues will be discussed on Jan. 18 and on consequitive PPPL seminars).

For the first time in the quasi-stationary fusion, LiWall concept
provides a consistent approach for solving both  problems of
power extraction. It also opens for US fusion program practically

             unlimited RESEARCH capabilities

(presumably, up to ignition and burning plasmas)
on tokamaks with the Li coated copper walls.

The presentation makes obvious to broad audience of physicists the
progmatic and scientific meaningless of continuing the  "compact"
stellarator project in PPPL.

2001, Jan. 11 "On new reality in tokamak physics and fusion" ("Necessity (a) of initiating LiWall research program and (b) terminating the "compact" stellarator project (NCSX)") - (link to .html file with my message of Jan.11, 2001 to US  fusion leaders and administraton and LiW US contributors). LiWalls started their offense for implementing new reality in the best fusion Lab in the World, PPPL.

Tokamaks with Lithium covered walls. Year 2000 (-> top)

2000,Dec.12, University of Texas, Austin, TX, Burning Plasma Workshop (Boudary physics discussion).
LiWall concept started to trace its research path to burning plasma and tokamak-reactor.
"Lithium Walls as the Plasma Facing Surface for the tokamak-reactors" -link to .ps file (link to .pdf file).

2000, Dec. 07, Princeton University, Physics Department Colloquium. LiWall concept broke the shell of cover up (created by PPPL manegment) and started to talk to physicists outside fusion.
"Tokamak Fusion, does it have a path ?"  -link to .ps file and .pdf  file (this .pdf is not a good conversion from .ps) . The file only  contains what  stayed behind
 the talk. It contains the most complete presentation of the LiWall concept at this moment.

    Absract of the PU talk

Tokamak fusion devices, which for 3 decades were leaders in the World
fusion program and which made a leap from 1 keV plasma
temperature in Russian T-3 machine (1968) to 40 keV
and 10.7 MW of DT fusion power in TFTR at PPPL (1994), are now in an
eventual state of defeat and possible shutdown in the US. Despite much
better understanding of the tokamak plasma now, many fundamental problems
on the way to the tokamak-reactor remain unresolved even at the
conceptual level. These problems include stability and steady state
plasma regime control, power extraction from both the plasma and the
neutron zone, activation and structural integrity of the machine under
14 MeV fusion neutron bombardment, maintenance of future reactors, etc.

This presentation describes the physics of a recently (Dec., 1998)
invented method of magnetic propulsion for driving liquid metal streams
in the tokamak magnetic field. This effect in combination with the idea
of renewable and absorbing walls at the plasma boundary (which
previously was only a theoretical abstraction) leads to  breaking with the
conventional approach to the tokamak fusion reactor. The resulting new
ideas, which in many aspects rely on the best US tokamak experiments on TFTR
(PPPL) and DIII-D (GA, San Diego) and basic theory, raise the hope on a
new research path for tokamaks toward a practical fusion reactor.

Tokamaks with lithium wall - a new way for tokamak fusion and tokamak science  ???

2000, Nov. 13-17, ALPS/APEX Meeting, Albuquerque, NM, SNL.  (4 talks) :

1. "Power extraction by liquid metal jets" (link to .ps file)   (link to .pdf file)
2. "Stabilization of tokamak plasma by lithium streams" (link to .ps file)  (link to .pdf file)
3. "Zinkle/Nelson Concept of Dual Lithium Stream First Wall/FLiBe blanket for tokamak-reactor" (link to .ps file)    (link to .pdf file)
 4. "Overview of TFTR Li experiments" (link to .ppt file)
(short version of D.Mansfield APS2000 presentation reported to APEX meeting by L.E.Zakharov)

2000, Oct.25-26 mini-Conference on Lithium Walls and Low Recycling Regimes, APS/DPP 2000, Quebec City, Canada,

"Lithium walls and Low Recycling Regimes in Tokamaks" - link to Agenda  of 2 day mini-Conference  with a number of  presentation titles linked to presentation files.

2000, May 08, ALPS/APEX Meeting (May 8-12) at Argonne Nat. Lab., Chicago IL, "Intense Lithium Streams in Tokamaks"  link to .ps file with presentation to APEX / ALPS(ALPS link may not work). Close loop for intense lithium streams in tokamak has been analyzed at a basic level. It was shown that lithium streams provide necessary power extraction capability for reactor applications. APEX ,  which initially rejected magnetic propulsion at Snowmass meeting, finally dropped its idea on liquid FLiBe first wall  in tokamaks as incompatible with plasma requirements. Also, the concept of thick liquid metal walls has been droped as incompatible with liquid metal MHD.

2000, May 09, ALPS/APEX Meeting (MAY 8-12) at Argonne Nat. Lab., Chicago IL,  "Proposal on Lithium Wall Experiment (LWX) on PBX-Mlink to presentation to on multi-institutional proposal for LiWall program in the US. PBX-M tokamak, the only one left in PPPL after distruction of TFTR and PLT, has been proposed as a test bed for the program.

Tokamaks with Lithium covered walls. Year 1999 (-> top)

1999, Sep. 09, US-Japan woorkshop on "High betas" (Sep. 8-20) at GA , San-Diego, CA, "The prospects for high-beta tokamaks with Li walls " link to presentation.  (Essense of the  non-recycling regime in eliminating thermo-conduction energy loss explained qualitatively,   Numerical calculations of pressure limits for this regime was presented).

"Magnetic propusion for driving liquid lithium walls"  link to 2-page long summary file on magnetic propulsion and associated issues  prepared for  1999 Fusion Summer Study  workshop in Snowmass  "Opportunities and Directions in Fusion Energy Science for the Next Decade" . Was excluded from final documents of the workshop by the fusion "opportunity seekers" disciminating everything, which does not fit the established status quo in the fusion program.

"A tokamak reactor with lithium walls"  link to 2-page long summary .ps file on the concept prepared for  1999 Fusion Summer Study workshop in Snowmass  "Opportunities and Directions in Fusion Energy Science for the Next Decade" .  Was excluded from final documents of the workshop by the fusion "opportunity seekers" disciminating everything, which does not fit the established status quo in the fusion program.

"Magnetic propulsion of liquid lithium in tokamaks"  Link to presentation to "IEA Workshop on Liquid Metal R & D for Fusion Applications" , Argonne NL IL, April 26, 1999. Not useful as repeats previous material. First presentation to technology ALPS  (link may nor work) people working on Advanced Limiter-divertor Plasma facing Surfaces. Collaboration with US technology side has been established.


 "Magnetic propulsion of conducting fluid and the theory of controlled tokamak reactor"   link to .ps file with the first presentation on magnetic propulsion to PPPL on Jan. 08, 99. Link is not  useful as it does not contain any pictures. Nevertheless, that time, the basic theory of magnetic propulsion has been developed and the new concept for tokamaks has been formulated. Also, for the first time, I raised clear objections of the administation decision to destroy TFTR and other tokamaks in PPPL which could acquire untouched potential if modified for lithium wall studies.

Numerical codes and the theory. (-> top)

Real Time Forecast (RTF) of tokamak discharges. (-> top)

 2004,  December 09, UKAEA Theory Colloquium (Culham, UK),  "Equilibrium reconstruction in eddy current environment in tokamaks"  In middle and small size tokamaks the eddy currents in the passive structures affect both the interpretation of magnetic signals and the plasma equilibrium. Complicated and essentially unpredictable current paths of eddies add a considerable problem to equilibrium reconstruction, one of the widely used tools fortokamak diagnostics.

 The presented theory introduces the response functions of magnetic signals as a necessary element of magnetic reconstruction.   The appropriate system of equilibrium reconstruction equations, which uses the time history of the discharge and signals, mitigates uncertainties associated with the eddy currents and allows for a proper weighting of equations. The theory gives a guidance for calibrating the magnetic diagnostics in tokamaks for purposes of equilibrium reconstruction as well as a method of recovering the response functions from measurements.

2004,  December 09
, EFDA-JET Seminar (Culham, UK), June 4, DIII-D Science Meeting(GA, CA San diago, CA), June 16, PPPL Research Seminar (Princeton, NJ)  "On Real Time Forecasts (RTF) of Tokamak Discharges" (.ps file, .pdf file)  This talk discusses the possibility to extend the existing experience with the real time equilibrium reconstruction by linking it with transport simulations and, thus, to approach the RTF of tokamak discharges. Unlike transport analysis codes (similar to "yesterday" weather analysis) or predictive codes ("next month" weather predictions), RTF targets a forecast of the plasma regime, e.g., in 0.1 tau_E (like the "next hour" weather predictions).

Three components,  crucial for RTF are discussed: (a) fast equilibrium calculations, (b) fast transport calculations for stiff models, and (c) computer assisted control of numerical codes and their communications, documentation, maintenance and interaction with other codes and drivers.
In this regard, (a) a new set of linearized equilibrium equations have been derived; (b) a shooting technique for stiff transport models has  been tested and shown to have two orders of magnitude faster convergence than the conventional implicit scheme; and (c) the CodeBuilder software for controlling the codes and communications was used for ESC-ASTRA-DCON-BALLLON code system as a RTF prototype.

The theory of Equilibrium reconstruction (-> top)

2007,  June 6, Russian Conference on High Temperature Plasma Diagnostics, Zvenigorod, Moscow region, RF,  "EquilibrZven070607.pdfium reconstruction of q- and p- profiles in ITER using different external and internal measurements", .ps2 file  .pdf file .pdf2 file.
Based on an earlier presentations (see below), the talk outlines a theory of variances in the reconstructions of the plasma current density and pressure profiles in the Grad-Shafranov equation. The associated technique was incorporated into the ESC code. Potential variances in q- and p- profiles have been calculated for different sets of external and internal measurements envisioned for equilibrium reconstruction in ITER.  It was shown that complementing the external magnetic measurements with either Stark line polarization signals (MSE-LP) or with recently proposed for ITER by Nova Photonics line shift signals (MSE-LS) can significantly improve the reliability of the reconstructed plasma profiles and the magnetic configuration.

Capabilities of calculating variances, incorporated into the numerical code ESC, have completed the theory of reconstruction, which for a long time  had a significant gap in ability to evaluate the quality of the presently widely used equilibrium reconstruction technique.

2007,  April 20, Science Meeting, General Atomic, San Diego CA,  "Consideration of variances in equilibrium reconstruction", .pdf file.
With small modications same as 2007,  March 20 talk (see below) to PPPL Experimental Seminar, Princeton NJ.

2007,  March 20, PPPL Experimental Seminar, Princeton NJ,  "The theory of equilibrium reconstruction and a possibility of complete reconstruction in ITER", .ps2 file  .pdf file .pdf2 file.
Potential variances in q- and p- profiles have been calculated for different sets of external and internal measurements envisioned for equilibrium reconstruction in ITER. It was shown that complementing the external magnetic measurements with either Stark line polarization signals (MSE-LP) or with recently proposed for ITER by Nova Photonics line shift signals (MSE-LS) can significantly improve reliability of reconstruction of plasma profiles and magnetic configuration. Capabilities of calculating variances, incorporated into numerical code ESC, have completed the theory of reconstruction, which for a long time  had a significant gap in ability to evaluate the quality of the presently widely used at present  equilibrium reconstruction technique.

2006,  August 08, PPPL Experimental Research Seminar, Princeton NJ, "The theory of variances of equilibrium current density reconstruction", .ps2 file  .pdf file .pdf2 file.  Same as the next on the page talk to EFDA-JET (with some corrections in calculations).

2006,  July 28
, EFDA-JET seminar, Culham Science Centre, Abingdon UK,  "The theory of variances of equilibrium current density reconstruction", .ps2 file  .pdf file .pdf2 file.
The talk presents a rigorous theory of uncertainties in the reconstructions of the plasma current density and pressure profiles in the Grad-Shafranov equation. The associated technique was incorporated into the ESC code, which provides the calculations of characteristic cases with different plasma cross-sections, aspect ratios and current distributions.

Equilibrium and associated codes for download (-> top)

2007, "Bishop-Taylor equlibria for calibration equilibrium and equilibrium reconstruction codes"
Feb 08, 2007 bsh.tgz  - Cbbsh code for calculation of the Bishop-Taylor equilibria (with the C-source and documentation).
Feb 08, 2007 tgz2bsh - script generating Cbbsh.

March 01, 2005 esc.tgz - Equilibrium and Stability Code (ESC)
March 01, 2005 tgz2esc - script generating Cbesc (the  CodeBuilder version of ESC)

2004, "Equilibrium Spline Interface (ESI) for magnetic confinement codes".

2002, "System of compact notations for numerical codes" ( .ps.pdf ) L.E.Zakharov, A.Pletzer, S. Galkin, A.S.Kukushkin.
A rigorous Name Generating System  (NGS) of  compact notations for math variables has been developed for both case sensitive (e.g., C) and case insensitive (e.g., FORTRAN) computer  codes.

 NGS-code ( ngs.Alpha,ngs.Sun, ngs.LinuxRH, ngs.c, (compile with cc -o ngs ngs.c))- name interpretation source code supplements the system. It accepts the  computer name from the keyboard, converts it into Latex format and displays the math interpretation of the name in an Xdvi window.  Download the appropriate version of the code, set an executable mode to its file and type the name of the executable.

Leonid Zakharov (zakharov@pppl.gov)