撕裂模不穩(wěn)定性65ppt課件

1、撕裂模不穩(wěn)定性線性實際平衡時的情況 邊境層構(gòu)造Y(Z)XZ(Y) MHD方程組磁流膂力學(xué)方程組0)()(0)(02PdtdtPttjBBBvBBjvv近似處置 不可緊縮條件近似，取消延續(xù)性方程 不思索能量方程壓力方程，做旋度消去壓力梯度，取消壓力方程。0 v)( MHD方程組磁流膂力學(xué)方程組2002()()02()0BPtt vBBBv BBv MHD方程組線性化磁流膂力學(xué)方程組00101102110( )exp(),()()0()yzxff xtik yik zffffi ft ekvBBBBBvBB 化簡第一項 取X分量化簡方程)()()()(10101201010210 xv vvvvv

2、xxxxxvvvvv101201010120)( 化簡第二項的X分量有關(guān)項 取X分量為留意到 化簡方程0110201100110)()()(BBkBBkBkkBBBkBkxxxBikiBiiBiixxxxxxBikiBBiBikiBBi10201101020110)()()()(kBBkkBkBBkkB 1110,xiB Bk B 化簡之后為 及 對于本征模，方程組有非零解，對應(yīng)增長率和波數(shù)之間的關(guān)系。 在知0階平衡量時，可數(shù)值求解。磁流膂力學(xué)方程組簡化xxxBviB12101)(BkxxxxBiBivv12010101200)( BkBk初態(tài)的平衡解 0階物理量應(yīng)該是MHD方程組的初態(tài)的平衡

3、解 下面是一組常用的解： 參數(shù)之間滿足000002( )( )( )tanh( )( )sec( )yyzzyzznxxBxBxBBaxxhaBeeee22000,22niTBBPconstm 無量綱方程： 這里S是磁Lundguist數(shù)，定義為 歸一化量：歸一化方程及無量綱參數(shù)210111()xxxBivBSk B22010 10101()xxxxvviBiB k Bk BDAAavS1,xAAvxkava數(shù)值求解方程 平衡的條件使得參數(shù)之間滿足XV1xXB1xea近似分析 在薄層外面，電流片之內(nèi)，電阻尚未起重要作用，S值大，增長率小，速度變化項可以忽略。 取平衡態(tài)的0階量之后，方程化為 解

4、析解為201100 xxBBkBkB2211(2sech)0 xxBkx B | |11(1tanh |)k xxBexkB1x 內(nèi)區(qū)求解，電阻率起作用，分散項主導(dǎo)，簡化為 同時，右邊第一項中的擾動磁場看為常數(shù)近似處置，成為可解的速度方程。式中各項都具有同樣數(shù)量級。 內(nèi)外區(qū)的解需求匹配。近似分析220111010()xxxxvBSBivi kBkB估算 真實情況分散區(qū)有一定厚度，但斜率躍變參數(shù)依然有意義。 內(nèi)區(qū)電阻率起作用，分散項主導(dǎo)，數(shù)量級估算為 消去e，求得2450513550() )()2aSkB111211(0 )(0 )222(0)(0)xxxxxBBBSSBBaaee e 0240

5、() )S ekB估算 有量綱情況表達(dá)如下： 另一種組合為 無量綱增長率隨著S的-0.6次方增長，與模擬結(jié)果一致。假設(shè)以分散時間歸一化，那么隨S的-0.4次方增長。134255550000.5()()kB 42132255555000.5()() )DAaakB 內(nèi)區(qū)方程為 近似取 經(jīng)過變量代換，可簡化為形如： 解析解為方程解析解2011010(0)()xxxvBiviS kBkB2 00()iix k Bk B1122401( )exp()(1)22dzzz 可以推導(dǎo)出類似的增長率表達(dá)式方程解析解4123245555550(1 / 4)()()(3 / 4)DAkBa 壓力、密度、磁場的平衡

6、關(guān)系 等離子體磁場越弱，撕裂模增長率越低壓力b值的影響2200000200015( )(1)22( )(1)2(1)iixBBTmm BxT非對稱情況21210( )tanh( )22BBBBxB xa 兩邊磁場非對稱時，OcK9H6E2B+y(u%rZoWlThQeNbJ8G4D1A-w*t$qYnVjSgPdLaI7F3C0y)v&s#pXmUiRfNcK9H5E2B+x(u$rZoWkThQeMbJ8G4D1z-w*t!qYnVjSgOdLaI6F3C0y)v%s#pXlUiRfNcK8H5E2A+x(u$rZnWkThPeMbJ7G4C1z-w&t!qYmVjRgOdL

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