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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Magnet Design Considerations for Fusion Nuclear Science Facility

The Fusion Nuclear Science Facility (FNSF) is a nuclear confinement facility that provides a fusion environment with components of the reactor integrated together to bridge the technical gaps of burning plasma and nuclear science between the International Thermonuclear Experimental Reactor (ITER) and the demonstration power plant (DEMO). Compared with ITER, the FNSF is smaller in size but generates much higher magnetic field, i.e., 30 times higher neutron fluence with three orders of magnitude longer plasma operation at higher operating temperatures for structures surrounding the plasma. Input parameters to the magnet design from system code analysis include magnetic field of 7.5 T at the plasma center with a plasma major radius of 4.8 m and a minor radius of 1.2 m and a peak field of 15.5 T on the toroidal field (TF) coils for the FNSF. Both low-temperature superconductors (LTS) and high-temperature superconductors (HTS) are considered for the FNSF magnet design based on the state-of-the-art fusion magnet technology. The higher magnetic field can be achieved by using the high-performance ternary restacked-rod process Nb3Sn strands for TF magnets. The circular cable-in-conduit conductor (CICC) design similar to ITER magnets and a high-aspect-ratio rectangular CICC design are evaluated for FNSF magnets, but low-activation-jacket materials may need to be selected. The conductor design concept and TF coil winding pack composition and dimension based on the horizontal maintenance schemes are discussed. Neutron radiation limits for the LTS and HTS superconductors and electrical insulation materials are also reviewed based on the available materials previously tested. The material radiation limits for FNSF magnets are defined as part of the conceptual design studies for FNSF magnets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Effects of magnetization on fusion product trapping and secondary neutron spectra

By magnetizing the fusion fuel in inertial confinement fusion (ICF) systems, the required stagnation pressure and density can be relaxed dramatically. This happens because the magnetic field insulates the hot fuel from the cold pusher and traps the charged fusion burn products. This trapping allows the burn products to deposit their energy in the fuel, facilitating plasma self-heating. Here, we report on a comprehensive theory of this trapping in a cylindrical DD plasma magnetized with a purely axial magnetic field. Using this theory, we are able to show that the secondary fusion reactions can be used to infer the magnetic field-radius product, BR, during fusion burn. This parameter, not ρR, is the primary confinement parameter in magnetized ICF. Using this method, we analyze data from recent Magnetized Liner Inertial Fusion experiments conducted on the Z machine at Sandia National Laboratories. We show that in these experiments BR ≈ 0.34(+0.14/−0.06) MG · cm, a ∼ 14× increase in BR from the initial value, and confirming that the DD-fusion tritons are magnetized at stagnation. This is the first experimental verification of charged burn product magnetization facilitated by compression of an initial seed magnetic flux.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Development of combined function dipole-quadrupole PMQs magnets for NSLS-II upgrade

This paper focuses on the R&D performed for the development of permanent magnets-based dipoles-quadrupoles combined function magnets (PMQs) for the future NSLSII upgrade “complex bend” lattice (CB). This new lattice uses PMQs that provide both bending (dipole) and strong focusing (quadrupole) magnetic field on the electron beam. The permanent magnet (PM) technology is suitable for the high magnetic field strengths (0.5 T, 130 T/m) required for such combine function magnets. PM technology leads to a compact magnet design that is essential in realizing the complex bend lattice concept, as well as a passive magnet solution which does not require electrical power supply reducing power consumption by ~ 80% (from 1.7 MW to 0.3 MW for NSLS-II). Two PMQs magnets designs are under consideration: A hybrid design that use both PM and soft iron poles, and Halbach type that is a pure PM design. Both PMQs designs present challenges in achieving the specified magnetic field quality due to their higher sensitivity to errors (mechanical tolerances and PM properties). This paper presents cost-effective designs and prototypes results for hybrid and Halbach PMQs, addressing various technical challenges while meeting the field requirements of the complex bend lattice for the NSLS-II upgrade.

N'gotta, Patrick [Brookhaven]↗
DOE OSTI2018

Anisotropic magnetic properties of the triangular plane lattice material TmMgGaO4

Highlights: • TmMgGaO{sub 4} crystallizes in the R-3m space group with the YbFe{sub 2}O{sub 4} structure. • TmMgGaO{sub 4} exhibits geometric magnetic frustration with no ordering down to 1.8 K. • Magnetic properties of TmMgGaO{sub 4} are highly anisotropic. - Abstract: The crystal growth, structure, and basic magnetic properties of TmMgGaO{sub 4} are reported. The Tm ions are located in a planar triangular lattice consisting of distorted TmO{sub 6} octahedra, while the Mg and Ga atoms randomly occupy intermediary bilayers of M-O triangular bipyramids. The Tm ions are positionally disordered. The material displays an antiferromagnetic Curie Weiss theta of ∼−20 −25 K, with no clear ordering visible in the magnetic susceptibility down to 1.8 K; the structure and magnetic properties suggest that ordering of the magnetic moments is frustrated by both structural disorder and the triangular magnetic motif. Single crystal magnetization measurements indicate that the magnetic properties are highly anisotropic, with large moments measured perpendicular to the triangular planes. At 2 K, a broad step-like feature is seen in the field-dependent magnetization perpendicular to the plane on applied field near 2 T.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Full particle orbit effects in regular and stochastic magnetic fields

Here we present a numerical study of charged particle motion in a time-independent magnetic field in cylindrical geometry. The magnetic field model consists of an unperturbed reversed-shear (non-monotonic q-profile) helical part and a perturbation consisting of a superposition of modes. Contrary to most of the previous studies, the particle trajectories are computed by directly solving the full Lorentz force equations of motion in a six-dimensional phase space using a sixth-order, implicit, symplectic Gauss-Legendre method. The level of stochasticity in the particle orbits is diagnosed using averaged, effective Poincare sections. It is shown that when only one mode is present, the particle orbits can be stochastic even though the magnetic field line orbits are not stochastic (i.e., fully integrable). The lack of integrability of the particle orbits in this case is related to separatrix crossing and the breakdown of the global conservation of the magnetic moment. Some perturbation consisting of two modes creates resonance overlapping, leading to Hamiltonian chaos in magnetic field lines. Then, the particle orbits exhibit a nontrivial dynamics depending on their energy and pitch angle. It is shown that the regions where the particle motion is stochastic decrease as the energy increases. The non-monotonicity of the q-profile implies the existence of magnetic ITBs (internal transport barriers) which correspond to shearless flux surfaces located in the vicinity of the q-profile minimum. It is shown that depending on the energy, these magnetic ITBs might or might not confine particles. That is, magnetic ITBs act as an energy-dependent particle confinement filter. Magnetic field lines in reversed-shear configurations exhibit topological bifurcations (from homoclinic to heteroclinic) due to separatrix reconnection. Finally, we show that a similar but more complex scenario appears in the case of particle orbits that depend in a non-trivial way on the energy and pitch angle of the particles.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

The importance of electrothermal terms in Ohm's law for magnetized spherical implosions

The magnetohydrodynamics (MHD) of magnetic-field compression in laser-driven spherical targets is considered. Magnetic-field evolution is cast in terms of an effective fluid velocity, a convective term resulting from resistivity gradients, a resistive diffusion term, and a source term. Effective velocity is the sum of fluid velocity, drift velocity, and heat-flux velocity, given by electron heat flux divided by electron enthalpy density, which has two components: the perpendicular or Nernst velocity and the cross-field velocity. The Nernst velocity compresses the magnetic field as the heat front moves into gas. The cross-field velocity leads to dynamo generation of an azimuthal magnetic field. It is proposed that the heat-flux velocity should be flux limited using a “Nernst” flux limiter independent of the thermal flux limiter but should not exceed it. The addition of the MHD routines to the 1D, Lagrangian hydrocode LILAC and the Eulerian version of the 2D hydrocode DRACO is described, and the codes are used to model a magnetized spherical compression on the OMEGA laser. Thermal flux limiting at a shock front is found to cause unphysical electron temperature gradients that lead to large, unphysical magnetic fields caused by the resistivity gradient, so thermal flux limiting in the gas is removed. The Nernst term reduces the benefits of magnetization in inertial fusion. A Nernst flux limiter ≤0.12 is required in the gas in order to agree with measured neutron yield and increases in the neutron-averaged ion temperature caused by magnetization. This corresponds to preventing the Nernst velocity from exceeding the shock velocity, which prevents significant decoupling of the magnetic field and gas compression.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1996

Computational Analysis of Static and Dynamic Behaviour of Magnetic Suspensions and Magnetic Bearings

Static modelling of magnetic bearings is often carried out using magnetic circuit theory. This theory cannot easily include nonlinear effects such as magnetic saturation or the fringing of flux in air-gaps. Modern computational tools are able to accurately model complex magnetic bearing geometries, provided some care is exercised. In magnetic suspension applications, the magnetic fields are highly three-dimensional and require computational tools for the solution of most problems of interest. The dynamics of a magnetic bearing or magnetic suspension system can be strongly affected by eddy currents. Eddy currents are present whenever a time-varying magnetic flux penetrates a conducting medium. The direction of flow of the eddy current is such as to reduce the rate-of-change of flux. Analytic solutions for eddy currents are available for some simplified geometries, but complex geometries must be solved by computation. It is only in recent years that such computations have been considered truly practical. At NASA Langley Research Center, state-of-the-art finite-element computer codes, 'OPERA', 'TOSCA' and 'ELEKTRA' have recently been installed and applied to the magnetostatic and eddy current problems. This paper reviews results of theoretical analyses which suggest general forms of mathematical models for eddy currents, together with computational results. A simplified circuit-based eddy current model proposed appears to predict the observed trends in the case of large eddy current circuits in conducting non-magnetic material. A much more difficult case is seen to be that of eddy currents in magnetic material, or in non-magnetic material at higher frequencies, due to the lower skin depths. Even here, the dissipative behavior has been shown to yield at least somewhat to linear modelling. Magnetostatic and eddy current computations have been carried out relating to the Annular Suspension and Pointing System, a prototype for a space payload pointing and vibration isolation system, where the magnetic actuator geometry resembles a conventional magnetic bearing. Magnetostatic computations provide estimates of flux density within airgaps and the iron core material, fringing at the pole faces and the net force generated. Eddy current computations provide coil inductance, power dissipation and the phase lag in the magnetic field, all as functions of excitation frequency. Here, the dynamics of the magnetic bearings, notably the rise time of forces with changing currents, are found to be very strongly affected by eddy currents, even at quite low frequencies. Results are also compared to experimental measurements of the performance of a large-gap magnetic suspension system, the Large Angle Magnetic Suspension Test Fixture (LAMSTF). Eddy current effects are again shown to significantly affect the dynamics of the system. Some consideration is given to the ease and accuracy of computation, specifically relating to OPERA/TOSCA/ELEKTRA.

Britcher, Colin P.↗
DOE OSTI2017

Friction consolidation of gas-atomized Fe−Si powders for soft magnetic applications

Soft magnetic materials are often limited in scalability due to conventional processes that do not retain beneficial microstructures, and their associated physical properties, during densification. In this work, friction consolidation (FC) has been studied to fabricate Fe−Si soft magnetic materials from gas-atomized powder precursors. Fe−Si powder is consolidated using variable pressure and tool rotation speed in an effort to evaluate this unique densification approach for potential improvements in magnetic properties. FC, due to the high shear deformation involved, is shown to result in uniform gradual grain structure refinement across the consolidated workpiece from the center nearest the tool to the edge. Magnetic properties along different orientations indicate little, if any, textural orientation in the refined grain structure. The effect of annealing on the magnetic properties is evaluated and shown to decrease coercivity. FC processing was able to retain the magnetization of the original gas-atomized powders but further process optimization is needed to reach the optimal coercivity for the soft magnetic materials applications. - Highlights: •Friction stir processing was utilized to consolidate Fe−Si soft magnetic powders. •The resultant microstructure and magnetic properties were correlated to the processing conditions. •Friction consolidation refined the grain size of the materials by ~ 40%. •Annealing successfully reduced the coercivity induced by the stress during processing. •The results shine light on the possible scaling up of nanostructured materials.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Magnetism in graphene oxide induced by epoxy groups

In this work, we have engineered magnetism in graphene oxide. Our approach transforms graphene into a magnetic insulator while maintaining graphene's structure. Fourier transform infrared spectroscopy spectra reveal that graphene oxide has various chemical groups (including epoxy, ketone, hydroxyl, and C-O groups) on its surface. Destroying the epoxy group with heat treatment or chemical treatment diminishes magnetism in the material. Local Density Approximation calculation results well reproduce the magnetic moments obtained from experiments, and these results indicate that the unpaired spin induced by the presence of epoxy groups is the origin of the magnetism. The calculation results also explain the magnetic properties, which is generated by the interaction between separated magnetic regions and domains. Our results demonstrate tunable magnetism in graphene oxide based on controlling the epoxy group with heat or chemical treatment.

36 MATERIALS SCIENCE↗
DOE OSTI2015

Magnetic and structural properties of ferromagnetic Fe{sub 5}PB{sub 2} and Fe{sub 5}SiB{sub 2} and effects of Co and Mn substitutions

Crystallographic and magnetic properties of Fe{sub 5}PB{sub 2}, Fe{sub 4}CoPB{sub 2}, Fe{sub 4}MnPB{sub 2}, Fe{sub 5}SiB{sub 2}, Fe{sub 4}CoSiB{sub 2}, and Fe{sub 4}MnSiB{sub 2} are reported. All adopt the tetragonal Cr{sub 5}B{sub 3} structure-type and are ferromagnetic at room temperature with easy axis of magnetization along the c-axis. The spin reorientation in Fe{sub 5}SiB{sub 2} is observed as an anomaly in the magnetization near 170 K and is suppressed by substitution of Co or Mn for Fe. The silicides are found to generally have larger magnetic moments than the phosphides, but the data suggest smaller magnetic anisotropy in the silicides. Cobalt substitution reduces the Curie temperatures by more than 100 K and ordered magnetic moments by 16%–20%, while manganese substitution has a much smaller effect. This suggests Mn moments align ferromagnetically with the Fe and that Co does not have an ordered moment in these structures. Anisotropic thermal expansion is observed in Fe{sub 5}PB{sub 2} and Fe{sub 5}SiB{sub 2}, with negative thermal expansion seen along the c-axis of Fe{sub 5}SiB{sub 2}. First principles calculations of the magnetic properties of Fe{sub 5}SiB{sub 2} and Fe{sub 4}MnSiB{sub 2} are reported. The results, including the magnetic moment and anisotropy, are in good agreement with experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Magnetic pinning in a superconducting film by a ferromagnetic layer with stripe domains

A magnetic study of superconductor/ferromagnet bilayers was performed by hysteresis loops and temperature-dependent magnetization measurements. The superconductor/ferromagnet bilayers consist of a Nb film deposited on a Py film with weak perpendicular magnetic anisotropy. By comparing the temperature-dependent magnetization data obtained on samples with different ferromagnetic layer thickness, a decrease of the magnetic pinning with increasing thickness of the ferromagnetic layer has been found. This is confirmed by the reduction of the Nb film critical current density at low fields extracted by using the magnetic irreversibility of the hysteresis loops. Here, the reduction of the pinning can be related to the increase of the stripe width in the ferromagnetic layer observed by magnetic force microscopy (MFM) measurements.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Magnetic hardening of Ce1+xFe11-yCoyTi with ThMn12 structure by melt spinning

A recent study on the intrinsic magnetic properties of CeFe11-yCoyTi has revealed that substituting one Co for Fe retains the favorable magnetocrystalline anisotropy H-a found in the ternary Fe end member, while enhancing the Curie temperature T-c and saturation magnetization 4 pi M-s. These findings warrant further optimization around Co substitution y = 1 to try to exploit the hard magnetic properties of these Ce-based magnets. Both Ce and Co concentrations in Ce1+xFe11-yCoyTi have been optimized in the range of x = 0 0.2 and y = 0 1.5. It was found that Co substitution effectively enhances all hard magnetic properties, although the values are still lower than those predicted from the intrinsic magnetic properties. Specifically, Tc increases from 210 degrees C to 285-350 degrees C; 4 pi M-19 (magnetization at 19 kOe) from 8.9 kG to 10.5-11.5 kG, remanence B-r from 3.1 kG to 4.1-4.5 kG, and most importantly, H-ci from 1.1 kOe to 1.5 kOe. As a result, the room temperature energy product (BH)(max) has been increased by over 100% from 0.7 MGOe in Ce1.1Fe11Ti to 1.5 MGOe in Ce1.05Fe9.75Co1.25Ti. Microscopy analysis indicates that the addition of Co refines the grain size and promotes chemical homogeneity at the microscopic scale. The beneficial effect of Co on the microstructure contributes to the improved hard magnetic properties. (C) 2015 AIP Publishing LLC.

Zhou, C↗
DOE OSTI2013

Crystal structure and magnetic properties of the Ba{sub 3}TeCo{sub 3}P{sub 2}O{sub 14}, Pb{sub 3}TeCo{sub 3}P{sub 2}O{sub 14}, and Pb{sub 3}TeCo{sub 3}V{sub 2}O{sub 14} langasites

We report the structural and magnetic characterizations of Ba{sub 3}TeCo{sub 3}P{sub 2}O{sub 14}, Pb{sub 3}TeCo{sub 3}P{sub 2}O{sub 14}, and Pb{sub 3}TeCo{sub 3}V{sub 2}O{sub 14}, compounds that are based on the mineral dugganite, which is isostructural to langasites. The magnetic part of the structure consists of layers of Co{sup 2+} triangles. Nuclear and magnetic structures were determined through a co-refinement of synchrotron and neutron powder diffraction data. In contrast to the undistorted P321 langasite structure of Ba{sub 3}TeCo{sub 3}P{sub 2}O{sub 14}, a complex structural distortion yielding a large supercell is found for both Pb{sub 3}TeCo{sub 3}P{sub 2}O{sub 14} and Pb{sub 3}TeCo{sub 3}V{sub 2}O{sub 14}. Comparison of the three compounds studied along with the zinc analog Pb{sub 3}TeZn{sub 3}P{sub 2}O{sub 14}, also characterized here, suggests that the distortion is driven by Pb{sup 2+} lone pairs; as such, the Pb compounds crystallize in a pyroelectric space group, P2. Magnetic susceptibility, magnetization, and heat capacity measurements were performed to characterize the magnetic behavior. All three compounds become antiferromagnetic with Néel temperatures T{sub N}≈21 K (Ba{sub 3}TeCo{sub 3}P{sub 2}O{sub 14}), ≈13 K (Pb{sub 3}TeCo{sub 3}P{sub 2}O{sub 14}), and ≈8 K (Pb{sub 3}TeCo{sub 3}V{sub 2}O{sub 14}), and they exhibit magnetic transitions at high applied magnetic fields, suggesting intrinsically complex magnetic behavior for tetrahedrally coordinated d{sup 7} Co{sup 2+} in this structure type. - Graphical abstract: Ba{sub 3}TeCo{sub 3}P{sub 2}O{sub 14}, Pb{sub 3}TeCo{sub 3}P{sub 2}O{sub 14} and Pb{sub 3}TeCo{sub 3}V{sub 2}O{sub 14} exhibit a triangles-of-triangles arrangement of the magnetic cations. Despite the Pb-induced crystallographic distortion, all of these materials exhibit competing antiferromagnetic and ferromagnetic interactions that lead to complex high field magnetism. - Highlights: • Nuclear and magnetic structures of Ba{sub 3}TeCo{sub 3}P{sub 2}O{sub 14}, Pb{sub 3}TeCo{sub 3}P{sub 2}O{sub 14} and Pb{sub 3}TeCo{sub 3}V{sub 2}O{sub 14}. • Structural characterization shows complex Pb-induced distortion. • Distortion puts Pb-compounds into space group that allows potential multiferroicity. • Magnetic characterization shows competing magnetic interactions. • Triangles of triangles motif results in complex high-field magnetic behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Magnetic properties and hyperfine interactions in Cr{sub 8}, Cr{sub 7}Cd, and Cr{sub 7}Ni molecular rings from {sup 19}F-NMR

A detailed experimental investigation of the {sup 19}F nuclear magnetic resonance is made on single crystals of the homometallic Cr{sub 8} antiferromagnetic molecular ring and heterometallic Cr{sub 7}Cd and Cr{sub 7}Ni rings in the low temperature ground state. Since the F{sup −} ion is located midway between neighboring magnetic metal ions in the ring, the {sup 19}F-NMR spectra yield information about the local electronic spin density and {sup 19}F hyperfine interactions. In Cr{sub 8}, where the ground state is a singlet with total spin S{sub T} = 0, the {sup 19}F-NMR spectra at 1.7 K and low external magnetic field display a single narrow line, while when the magnetic field is increased towards the first level crossing field, satellite lines appear in the {sup 19}F-NMR spectrum, indicating a progressive increase in the Boltzmann population of the first excited state S{sub T} = 1. In the heterometallic rings, Cr{sub 7}Cd and Cr{sub 7}Ni, whose ground state is magnetic with S{sub T} = 3/2 and S{sub T} = 1/2, respectively, the {sup 19}F-NMR spectrum has a complicated structure which depends on the strength and orientation of the magnetic field, due to both isotropic and anisotropic transferred hyperfine interactions and classical dipolar interactions. From the {sup 19}F-NMR spectra in single crystals we estimated the transferred hyperfine constants for both the F{sup −}-Ni{sup 2+} and the F{sup −}-Cd{sup 2+} bonds. The values of the hyperfine constants compare well to the ones known for F{sup −}-Ni{sup 2+} in KNiF{sub 3} and NiF{sub 2} and for F{sup −}-Cr{sup 3+} in K{sub 2}NaCrF{sub 6}. The results are discussed in terms of hybridization of the 2s, 2p orbitals of the F{sup −} ion and the d orbitals of the magnetic ion. Finally, we discuss the implications of our results for the electron-spin decoherence.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2006

Magnetic Causes of Solar Coronal Mass Ejections: Dominance of the Free Magnetic Energy over Either the Magnetic Twist or Size Alone

We report further results from our ongoing assessment of magnetogram-based measures of active-region nonpotentiality and size as predictors of coronal mass ejections (CMEs). We have devised improved generalized measures of active-region nonpotentiality that apply to active regions of any degree of magnetic complexity, rather than being limited to bipolar active regions as our initial measures were. From a set of approx.50 active-regions, we have found that measures of total nonpotentiality have a 75-80% success rate n predicting whether an active region will produce a CME in 2 days after the magnetogram. This makes measures of total nonpotentiality a better predictor than either active-region size, or active region twist (size-normalized nonpotentiality), which have a approx.65% success rates. We have also found that we can measure from the line-of-sight magnetograms an active region's total nonpotentiality and the size, which allows use to use MDI to evaluate these quantities for 4-5 consecutive days for each active region, and to investigate if there is some combination of size and total nonpotentiality that have a stronger predictive power than does total nonpotentiality. This work was funded by NASA through its LWS TR&T Program and its Solar and Heliospheric Physics SR&T Program, and by NSF through its Solar Terrestrial Research and SHINE programs.

Falconer, D. A.↗
NASA NTRS2018

Percolation Behaviour in the Magnetic Permeability and Electrical Conductivity in Conducting Magnetic - Insulating Non Magnetic Binary Composites

Experimental results of the complex magnetic permeability (µ) and the electrical conductivity (σ) of a granular paramagnetic Gadolinium Gallium Garnet (GGG: 0.3–26 vol%) and Teflon (PTFE) system are presented and discussed in relation to previously published (conductivity) and unpublished (permeability) studies on granular Fe3O4 – talc and Ni – talc wax systems. In these systems plots of the real conductivity (σ'(sub m)) against the volume fraction (φ) lie on characteristic sigmoid curves that when fitted to the Two Exponent Phenomenological Percolation Equation (TEPPE) confirm the existence of “percolation microstructures” with critical volume fractions (φ(sub c)). The plots of the real and imaginary permeability (µ'(sub m)) and (µ"(sub m)) satisfactorily fit to the TEPPE using the φ(sub c) obtained in each case from the “conductivity” measurements. In all three cases the conductivity results gave the exponent t > 2, and the permeability results gave t < 1.

David S McLachlan↗