W.W. Engelhardt

JET, Max-Planck-Institut für Plasmaphysik (retired) · ED2, E3

Faraday's law of induction and Maxwell's flux law are used to construct Poynting's theorem which is supposed to describe the flow of electromagnetic energy into the direction of the Poynting vector. It is shown that this theory fails already in the simplest cases of resistive or super conducting wires.

This is the published version in International Journal of Science and Research Methodology of the manuscript posted in May 2019

The Event Horizon Telescope (EHT) consists in effect of several Michelson stellar interferometers. The separation of the radio antennae is up to 10000 km, but the received signals from M87* are still coherent. This means that the observed object is smaller than the resolving power of the virtual telescope. Thus, neither the width of the object nor...

The Event Horizon Telescope (EHT) consists in effect of several Michelson stellar interferometers. The separation of the radio antennae is up to 10000 km, but the received signals from M87* are still coherent. This means that the observed object is smaller than the resolving power of the virtual telescope. Thus, neither the width of the object nor...

Sfarti's rebuttle of my paper rejected.

A contemplation on the detection of gravitational waves in three different places on August 14, 2017.

The uncertainties concerning LIGO's alleged discovery of the gravitational wave GW150914 (PRL 116, 061102 (2016)) have not been removed during the past year. The calibration e-print arXiv:1602.03838v1 [gr-qc] 11 Feb 2016 was not published in a peer reviewed journal, and is not listed among the RG contributions of two prominent co-autthors: Prof. B....

Einstein's explanation of Mercury's perihelion motion has been verified by astronomical observations. His formula could also be obtained in Schwarzschild metric and was published already in 1898. Motion along a straight geodesic, however, namely free fall into a gravitational centre with vanishing angular momentum, is incorrectly described both by...

Einstein's own demonstration of time dilation taken from his book with L. Infeld [A. Einstein and L. Infeld, The Evolution of Physics (Cambridge University Press, U.K., 1938)] is analyzed. His ingenious circumnavigation of an apparent discrepancy between clock synchronization and Lorentz transformation is discussed.

Both the classical and the relativistic composition law for velocities are applied to re-calculate the Sagnac Effect. The ensuing formulae for the fringe shift are found to differ already in first order of v/c. Whilst the classical formula is validated by interferometric measurements and verified by the GPS-system, this is not the case for the rela...

Patrick Illinger wrote a comment in SZ: “Wie dumm sind wir eigentlich” (“How stupid are we in actual fact?”) He took reference to a number of scientific frauds that remained undiscovered for quite a while. This letter tries to make him aware of the actual case: The “discovery” of gravitational waves. At the moment there is just a claim of LIGO who...

The Nobel Committee is informed that according to Professor Karsten Danzmann (Albert Einstein Institut) the LIGO detectors are not calibrated as expected from the statement in the discovery paper: "The detector output is calibrated in strain by measuring its response to test mass motion induced by photon pressure from a modulated calibration laser...

This letter to Christopher Schrader was written in response to his article "Mensch und Mythos" dealing with Einstein's General Theory of Relativity (http://www.sueddeutsche.de/wissen/wissenschaftsgeschichte-mensch-und-mythos-1.2664281). Sueddeutsche Zeitung have given permission to reproduce here the original article for a limited period of time.

The relation between electric field and current density in Ohm's law is different in structure compared to the connection following from Maxwell's equations between the same vector fields. The compatibility of the different relationships is investigated for static and quasistatic situations. It is found that, in general, the electric field in Ohm's...

This letter to Christopher Schrader was written in response to his article "Mensch und Mythos" dealing with Einstein's General Theory of Relativity (http://www.sueddeutsche.de/wissen/wissenschaftsgeschichte-mensch-und-mythos-1.2664281). Sueddeutsche Zeitung have given permission to reproduce here the original article for a limited period of time....

According to CED the electrodynamic fields depend exclusively on the charge and the velocity of particles. They do not depend on the mass of the charged moving particles. The Lorentz force models the interaction between the fields and ponderable matter. If this description were exact, a violation of the conservation of momentum would occur. A demon...

Maxwell's displacement current - a parable in his equations (Research note of 2002)

A new interpretation of the famous Pound-Rebka experiment: "Apparent Weight of Photons" (https://en.wikipedia.org/wiki/Pound%E2%80%93Rebka_experiment) in terms of a variable velocity of light dependent on the gravitational potential. (Research note of 2001).

Available from arXiv.org: http://arxiv.org/abs/1506.09070

Einstein's own demonstration of time dilation taken from his book with L. Infeld (1938) is analyzed. His ingenious circumnavigation of an apparent discrepancy between clock synchronisation and Lorentz transformation is discussed.

This is an abbreviated version of my paper "Einstein's Third postulate" ( http://arxiv.org/abs/1506.09070) in German language. Since Oct. 20, 2016 there exists also an English translation of this note: https://www.researchgate.net/publication/309312005_Einstein%27s_own_refutation_of_his_theory?ev=prf_pub

Upon request of Barry Turner (Universityof Lincoln) I have produced an English translation of the note: https://www.researchgate.net/publication/282325187_Einsteins_eigene_Widerlegung_seiner_Theorie?ev=prf_pub

Upon BarryTurner's (University of Lincoln) request I have produced an English translation of the note: https://www.researchgate.net/publication/282325187_Einsteins_eigene_Widerlegung_seiner_Theorie?ev=prf_pub

The interaction between charged particles through quasi-static fields must occur instantaneously; otherwise a violation of the energy principle would occur. As a consequence, the instantaneous transmission of both energy and information over macroscopic distances is feasible by using the quasi-static fields which are predicted by Maxwell's equation...

Let us perform a gedanken experiment that was Einstein's favourite method of doing research. Suppose there are two twin trains of identical construction, each 10 km long, equipped with precise clocks in the last and in the first waggon. One train is in System K, the other one in K'. The coordinates of the last waggons are x = x' = 0 and those of th...

The interaction between charged particles through quasi-static fields must occur instantaneously; otherwise a violation of the energy principle would occur. As a consequence, the instantaneous transmission of both energy and information over macroscopic distances is feasible by using the quasi-static fields which are predicted by Maxwell's equation...

In Maxwell’s classical theory of electrodynamics the fields are frequently expressed by potentials in order to facilitate the solution of the first order system of equations. This method obscures, however, that there exists an inconsistency between Faraday’s law of induction and Maxwell’s flux law. As a consequence of this internal contradiction th...

Traditionally, the outcome of Michelson's interference experiment has been interpreted as evidence against the existence of a luminiferous medium called “ether.” Einstein, however, emphasized in 1920 that an ether must exist in spite of Michelson's null result. In this paper, it is shown that a medium theory—be it for light or for sound—actually pr...

An algorithm allowing a fast solution of stationary and time dependent 1-d diffusion problems for the case of finite ionization and recombination rates is presented. Results of numerical computations and an analytic stability analysis show its unconditional stability. The computational effort involved rises only linearly with the number of ionizati...

Both the classical and the relativistic composition law for velocities are applied to re-calculate the Sagnac Effect. The ensuing formulae for the fringe shift are found to differ already in first order of v/c. Whilst the classical formula is validated by interferometric measurements and verified by the GPS-system, this is not the case for the rela...

The Lorentz Transformation, which is considered as constitutive for the Special Relativity Theory, was invented by Voigt in 1887, adopted by Lorentz in 1904, and baptized by Poincar\'e in 1906. Einstein probably picked it up from Voigt directly.

Complementing a study which was published in this journal in 2005, we present explicit calculations of fields predicted by Maxwell's equations both in Lorenz and in Coulomb gauge. Analytic expressions are obtainable, when the source of the fields is an oscillating electric dipole. As before it is found that the fields calculated by different method...

In Maxwell's classical theory of electrodynamics the fields are frequently expressed by potentials in order to facilitate the solution of the first order system of equations. This method obscures, however, that there exists an inconsistency between Faraday's law of induction and Maxwell's flux law. As a consequence of this internal contradiction th...

In this comment it is demonstrated that contrary to the claim in the title, 'Electromagnetic potentials without gauge transformations', the potentials were actually calculated in the Coulomb gauge.

During the Ohmic Heating Phase of JET operation (June 1983 – September 1984), impurities in the plasma have been studied by visible and VUV spectroscopy, and from bolometer and soft X-ray signals. The measurements provide information on impurity influxes and impurity densities in the plasma. Plasma dimensions and parameters were a = 1.1 m, b = 1.3–...

Observations of theta-pinch plasmas were followed up by calculating the energy losses due to resonance line radiation from oxygen impurities. A plasma, homogeneous in density and temperature, was assumed to be heated instantly from a low initial temperature to a certain high temperature. The oxygen atoms are thereby ionized over different ionizatio...

The frequency shifts predicted by the 'relativistic' Doppler effect are derived in the photon picture of light. It turns out that, in general, the results do not depend exclusively on the relative velocity between observer and light source. In this respect, the relativistic Doppler effect is not distinct from the classical one, where the shifts are...

The potential concept that is successful in classical electrodynamics should also be applicable to the nonlinear electromagnetic forces acting on matter. The obvious method of determining these potentials should be provided by Helmholtz's theorem. It is found, however, that the theorem fails in most practical instances. Other methods to find the po...

In an attempt to solve Maxwell's first order system of equations, starting from a given initial state, it is found that a consistent solution depending on the temporal evolution of the sources cannot be calculated. The well known retarded solutions of the second order equations, which are based on the introduction of potentials, turn out to be in d...

The interaction between charged particles through quasi-static fields must occur instantaneously; otherwise a violation of the energy principle would occur. As a consequence, the instantaneous transmission of both energy and information over macroscopic distances is feasible by using the quasi-static fields which are predicted by Maxwell's equation...

The concept of gauge invariance in classical electrodynamics assumes tacitly that Maxwell’s equations have unique solutions. By calculating the electromagnetic field of a moving particle both in Lorenz and in Coulomb gauge and directly from the field equations we obtain, however, contradicting solutions. We conclude that the tacit assumption of uni...

Classical plasmas in thermodynamic equilibrium should be neither para- nor diamagnetic due to the action of the Lorentz force. Magnetic confinement, however, is based on the observed diamagnetism of laboratory plasmas. The apparent paradox is investigated on the basis of the resistive magneto-hydrodynamic equations. It is found that, at least in si...

The calculation of both resistive and ideal plasma equilibria amounts to solving a number of magnetic differential equations which are of the type $\vec {B}\cdot \nabla \Phi =s$. We apply the necessary and sufficient criterion for the existence of the potential $\Phi$ and find that a static equilibrium configuration of a magnetically confined plasm...

Introduction Classical electrodynamics, as it is taught today [1], is based on Hertz's formulation [2] of Maxwell's field equations for matter at rest, and on the Lorentz force which describes the action of the fields on electric particles. It appears unnecessary to formulate an electrodynamics for moving matter, as Hertz attempted in his second pa...

By investigating the motion of a point charge in an electro-static and in a magnetostatic field, it is shown that the rel-ativistic transformation of electromagnetic fields leads to ambiguous results. The necessity for developing an 'elec-trodynamics for moving matter' is emphasized.

The frequency shifts predicted by the `relativistic' Doppler e#ect are derived in the photon picture of light. It turns out that, in general, the results do not depend exclusively on the relative velocity between observer and light source.

Several experiments were conducted in ASDEX Upgrade to prove the suitability of tungsten as a divertor target material under the conditions of a high density and low temperature divertor. The observed fluxes from a tungsten tile into the plasma are low, in keeping with the extremely low sputtering yields. In addition, the very favourable effect of...

Tungsten was injected by means of laser ablation in both ohmic and additionally heated plasmas of the ASDEX Upgrade tokamak experiment. Spectroscopic investigations were performed in the extreme ultraviolet (EUV) wavelength region, 4 to 140 nm. Besides the quasi-continuum structure at ≈ 5 nm emitted by tungsten ions around W27+, isolated lines of t...

The closed ASDEX Upgrade Divertor II, `LYRA', is capable of handling heating powers of up to 20 MW or P/R of 12 MW/m, owing to a reduction of the maximum heat flux to the target plates by more than a factor of 2 compared with the open Divertor I. This reduction is caused by high radiative losses from carbon and hydrogen inside the divertor region a...

Presents an overview of the main results obtained on JET. The author deals with the measures to control the impurity contamination and the resulting wall and limiter conditions. The impurity situation during ohmic discharges is reviewed and the main effects resulting from auxiliary heating are given.

JET tokamak performance has been progressively raised, culminating in operation at the full design level of 5 MA plasma current in a toroidal field at 3.4 T. the plasma current, position, shape and line-average electron density are controlled by feed-back systems. By glow discharge cleaning in H2/methane mixtures, the interior of the vessel has bee...

There exist two classes of discharges on ASDEX which overcome the severe confinement deterioration at high densities or heating power. The first class is characterized by unusually peaked density profiles and the second one by exceptionally broad ones. These profiles and the concomitant confinement enhancement imply a change in both the particle an...

Tungsten-coated tiles, manufactured by plasma spray on graphite, were mounted in the divertor of the ASDEX Upgrade tokamak and cover almost 90% of the surface facing the plasma in the strike zone. Over 600 plasma discharges have been performed to date, around 300 of which were auxiliary heated with heating powers up to 10 MW. The production of tung...

ASDEX Upgrade is a poloidal divertor experiment very similar to ITER with respect to magnetic field properties and especially to the plasma boundary geometry. A large part of the programme on ASDEX Upgrade is therefore dedicated to investigating and optimizing reactor-relevant plasma boundary issues. This contribution is concerned with H-mode studi...

The completely detached high confinement (CDH) regime established recently in high power ASDEX-Upgrade single null divertor discharges is described. The standard CDH mode scenario with feedback controlled external deuterium and neon puffing is analysed in detail with respect to its divertor detachment and confinement properties. Impurity transport...

Densities achievable in ASDEX Upgrade discharges are restricted by a disruptive limit in the L-mode caused by an edge-power imbalance which is linking divertor detachment, Marfe formation and the separatrix density. The attainable average densities depend then on the internal particle sources and the core transport and can exceed the empirical Gree...

Tungsten coated tiles, manufactured by plasma spray on graphite, were mounted in the divertor of the ASDEX Upgrade tokamak and cover almost 90% of the surface facing the plasma in the strike zone. Over 500 plasma discharges, among which around 300 were heated with heating powers up to 10 MW, were performed up to now. The tungsten flux in the divert...

Feedback-controlled puffing of neon and deuterium has been applied to control the edge-localized-mode behavior and the target plate power deposition during high-power H-mode discharges in ASDEX Upgrade. A regime has been found in which more than 90% of the heating power is lost through radiation and divertor detachment occurs, without deterioration...

Feedback-controlled puffing of neon and deuterium has been applied to control the edge-localized mode behavior and the target plate power deposition during high-power H-mode discharges in ASDEX Upgrade. A regime has been found in which more than 90% of the heating power is lost through radiation and divertor detachment occurs, without deterioration...

The results of divertor studies on ASDEX Upgrade, at currents of up to 1.2 MA and heating powers up to 10 MW are described, with emphasis on the ELMy H-mode. The spatial and temporal characteristics of their heat load, and the simulation of ELMs by a time-dependent scrape-off layer code are described. High gas puff rates were found to lead to a lar...

Applying the magnetohydrodynamic equations of a plasma to a superconductor the phenomenological London equation describing the Meissner-Ochsenfeld effect is classically interpreted as representing a unique equilibrium state of the current distribution.

Essential divertor functions - density and energy control - have been investigated in the JT-60 divertor with metal walls. Neutral pressure in the divertor chamber increases in proportion to n ̄2e and high recycling state for particle exhaust is realized. At ne ≤ 6 × 1019 m-3, wall pumping by the divertor plates is dominant in particle exhaust. How...

Impurities in fusion plasmas have two detrimental effects that may render the achievement of ignition difficult: dilution of the reacting plasma reduces the produced fusion power and radiation losses prevent efficient heating up to ignition temperatures. In tokamaks, impurities are released from the containing vessel walls by plasma--wall interacti...

Ohmic heating studies in hydrogen and deuterium up to currents of Ip = 5 MA have been completed and additional heating experiments by means of ICRH and NBI are now in process. With ICRH powers up to 7 MW, the global energy confinement time τE is observed to deteriorate with increasing heating power. NBI experiments are at a more preliminary stage,...

Heating the JET plasma well above temperatures reached in the ohmic phase is the aim of the two additional heating systems planned for JET: ion cyclotron resonance heating (ICRF) and neutral beam injection (NBI). Operations with the latter started in February 1986, initially with hydrogen injection, up to a power level of 7 MW. ICRF power has been...

The rapid collapse of a sawtooth oscillation in the JET tokamak has been observed in detail on a fast time scale. Tomographic reconstruction of data from two x-ray cameras and electron-cyclotron-emission temperature profiles show that during the sawtooth collapse the central hot region is rapidly (in ~=100 mus) displaced off axis with an m=1 compon...

After five years of construction JET started its operation in June 1983. In December plasmas with peak currents of 3 MA were produced. Flat top times of a few seconds were obtained for currents of 2.4 MA. The plasmas were slightly elongated ( ~ 20%) with a minor radius of about 1 m. Line densities (peak values) reached 7 × 1019 m−2, electron temper...

First results from neutral beam heating of diverted ASDEX discharges are being reported. The experiments have been performed at 1.25 MW and 2.6 MW of neutral power injected into divertor-assisted plasmas at line-averaged densities between 2 and 4 × 1013 cm-3 at Ip1 = 320 kA and BT = 2.2 T. Ion temperatures up to 3.5 keV and electron temperatures up...

A toroidal large area limiter was installed in the divertor tokamak ASDEX. The limiter basically consists of a plane annular stainless steel sheet which is tangential to the plasma and which is placed in the bottom of the main plasma chamber. In a second series of experiments this limiter was covered with graphite plates.With the steel limiter clea...

The fueling efficiency for gas puffing, i.e. the fraction of the external gas flux that is ionized inside the separatrix, is reduced in divertor discharges since part of it is ionized in the scrape-off layer and pumped off by the divertor. The fueling efficiency is determined by switching-off the gas feed during the stationary phase of a discharge...

The divertor efficiency in ASDEX is discussed for ohmically heated plasmas. The parameters of the boundary layer both in the torus midplane and the divertor chamber have been measured. The results are reasonably well understood in terms of parallel and perpendicular transport. A high pressure of neutral hydrogen builds up in the divertor chamber an...

A new operational regime has been observed in neutral-injection-heated ASDEX divertor discharges. This regime is characterized by high βp values comparable to the aspect ratio A(βp<~0.65A) and by confinement times close to those of Ohmic discharges. The high-βp regime develops at an injection power ≥1.9 MW, a mean density n¯e>~3×1013 cm−3, and a q(...

Three lectures given during Course 6.-17. September 1982 on DIAGNOSTICS FOR FUSION REACTOR CONDITIONS at INTERNATIONAL SCHOOL OF PLASMA PHYSICS

Use of the ASDEX divertor permits the production of stable low-density discharges (ne≳1012 cm-3) with extremely low resistivity lasting for more than 10 s. While the distribution functions of electrons and ions show suprathermal tails, runaway electrons in the megaelectronvolt range are found to disappear with decreasing density. There are indicati...

In the first experimental phase the divertor tokamak ASDEX was run with a closed SS-limiter. The cleaning procedure for the vessel consisted of baking to 120°C, carbon removal by glow discharge in hydrogen, and oxygen removal with a continuous low power 50 Hz AC discharge. Wall contact of the plasma was reduced by carefully positioning the plasma w...

The tearing mode stability of the radial profiles of current density resulting from the skin effect accompanying AC modulation is calculated using a computer program. An AC component was superposed on the plasma current and a computer program was designed to calculate the current distribution accompanying the AC modulation which takes into account...

At the end of high-density plateaus a strong accumulation of impurities by a factor of 5 within less than 10 ms is observed in Pulsator. This leads to a displacement of the current into an outer region with a subsequent steepening of the gradient at the q 2 surface. The resulting disruption prevents the production of longer density plateaus. From o...

The hard X-ray emission from the limiter of Pulsator tokamak shows three distinct types of intensity modulations: an oscillation correlated with the m 2 mode, strong sawtooth modulations coincident with the internal disruptions, and radiation bursts indicating an external disruption or a similar type of instability. For the purpose of interpretatio...

This work deals with the properties of an ergodic magnetic limiter and presents calculations concerning the reduction of the impurity rate in a tokamak by a boundary sheath with decreased confinement time. The layer is produced by resonant helical windings superposed on an equilibrium magnetic field with closed magnetic surfaces [1].The transport c...

The high- and Low-Z impurity make-up of the plasma both at Low and high density Tokamak discharges has been investigated. At 4 ms into the discharge the oxygen impurity content is estimated from the OVI (1032 Aring;) Line intensity to be about 3 % of the electron density. Later in the discharge the quantitative estimate of the oxygen content is mor...

In the Pulsator, the toroidal rotation of a helical m 1, m 2 system of increasing amplitude precedes the current disruption for a few milliseconds. In most cases, the m 1 and m 2 modes couple on the outside of the torus and rotate toroidally in the direction of the electron drift. After the perturbation reaches a certain amplitude, the central elec...

Conditions are investigated for stable operation of a Pulsator device at high density due to pulsed hydrogen inflow. The ion and electron contributions to the ratio between plasma kinetic pressure and magnetic pressure are estimated, and a ratio curve obtained experimentally with magnetic probes is used to calculate the energy confinement time. It...

New formulas for relevant relaxation times and relaxation lengths for the establishment of partial local thermal equilibrium are presented taking into consideration the influence of the ground state on the population of the excited levels and on the energy distribution of the free electron gas.