M. Ignatenko

M. Tanaka

Ignatenko,  M.

Tanaka,  M.

NIFS-Repository (National Institute for Fusion Science)

Numerical simulation of the mi-crowave heating of copper powders ina single mode cavityIgnatenko, M., and Tanaka, M. (Chubu Univ.)Recently the expression for the estimation of eﬀec-tive parameters of compacted powdered metals has beenobtained by means of the combination of Mie theory andBruggeman’s eﬀective medium1). For example, in thisapproach the eﬀective permeability μeﬀ is determinedby solving the equationsp μp − μeﬀμp + 2μeﬀ+ (1− p) μg − μeﬀμg + 2μeﬀ= 0, (1)where p is the volume fraction of particles; the perme-ability μg is the optical parameters of gas in pores; andμp = 2μ2 1− (r1/r2)3βa2 + (r1/r2)3βa , βa = 21− (μ1/μ2)F12 + (μ1/μ2)F1 . (2)Here, r1,2 are the radii of the metal core and the insulat-ing shell; ε1,2 and μ1,2 are the permittivity and perme-ability of the core and the shell, respectively. The factorF1 isF1(y) = 2 −y cos y + sin yy cos y − sin y + y2 sin y , (3)with y ≡ k1r1, where k1,2 = ω√ε1,2μ1,2, ω = 2πf , f isthe frequency of the incident wave.The estimated parameters of copper powders areshown in Table I. By means of the obtained parameters,the numerical simulation of the microwave heating of aspherical sample is performed. Radius of the sample is5 mm. Results of the calculations are shown in Fig. 1.When the sample is placed in the free-space standingwave, it is well heated by the H-ﬁeld but not by the E-ﬁeld component of the microwaves. Clearly, the externalelectric ﬁeld is perfectly screened out by conduction elec-trons in metals, and therefore it cannot heat the copperpowders. In contrast, the magnetic ﬁeld still penetratesby the skin-depth deep, and when the particle size in thepowder is small, as in the presented case, the dissipa-tion of the microwave energy due to Joule loss is strongenough to heat the powders.2)The situation is diﬀerent when the sample in thesample holder is placed in a single mode cavity. Parame-ters of the cavity are corresponded to those shown in theTable I: Parameters of the copper powders used in cal-culations (r2 − r1 = 50nm, p=0.5, f=2.45GHz, ε/ε0 =5 + i0.5, T= 270C).rparticle [μm] 1 10εeﬀ/ε0 27 + i2.7 252 + i25.2μeﬀ/μ0 0.99 + i0.05 0.46 + i0.12Keﬀ [W/K m] 43.3 9301002003004005006007008000 50 100 150 200 250 300T [C]t [s]WR284 TE102 r10p50SW_EmaxSW_HmaxWR284_EmaxWR284_HmaxTEmax(a)(b)01002003004005006007008000 50 100 150 200 250 300T [C]t [s]WR284 TE102 r01p50SW_EmaxSW_HmaxWR284_EmaxWR284_HmaxTEmaxFig. 1: Calculated heating history for the sample madeof (a) 10 μm and (b) 1 μm particles. Here, SW stands forfree-space standing wave, WR284 indicate the heating inthe single mode cavity.paper of Ma et al.3) Intensity of the E-ﬁeld is the sameas in the free-space standing wave. In this case, heatingrate in the E-ﬁeld maximum is enhanced while that inthe H-ﬁeld maximum is almost the same as in previouscalculations. Now, in some situations the sample is stillheated in the H-ﬁeld maximum much stronger than inthe E-ﬁeld one (Fig. 1(a)). At the same time, it is alsopossible the situation, when heating in the E-ﬁeld maximis stronger than that in the H-ﬁeld (Fig. 1(b)).The free-space results suggest that the enhancementof heating in the E-ﬁeld maximum is associated with theimperfect separation of the E-ﬁeld and H-ﬁeld compo-nents in the cavity. It means that experiments utilizingseparation of E and H-ﬁelds need to be performed care-fully.1) M. Ignatenko and M. Tanaka: Physica B 405 (2010)3522) M. Ignatenko, M. Tanaka and M. Sato:Jpn. J. Appl. Phys. 48 (2009) 0670013) J. Ma, J. F. Diehl, E. J. Johnson etc: J. Appl. Phys.101 (2007) 074906.436§15. Numerical Simulat on of the Microwave Heating of Copper Powders in a Single Mode CavityIgnatenko, M., Tanaka, M. (Chubu Univ.)

Numerical Simulation of the Microwave Heating of Copper Powders in a Single Mode Cavity

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