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Table 1

Nine sets of parameters for T&D models with different twist turns, embedded in a solar atmosphere with nonuniform β and Alfvén speed.

Case Feature I0 a α /Φc(a)a βmin/βin/βexb τ a c

refTDa Crash downward –9.5 0.32 1.0 2.454/5.247 0.023/0.032/0.088 0.21
htirep Expand outward –9.5 0.32 0. 5.247/5.247 0.023/9.850/0.088 0.21
ltirep Stable about 2τa –9.5 0.32 0.9 2.545/5.247 0.023/0.259/0.088 0.21
lowtwist Current redistribute –27.1 0.48 0.9 0.845/0.979 0.007/0.069/0.019 0.10
inftwist External kink 0. 0.48 0.96 2.275/ 0.033/0.097/0.369 0.43

refTDb Internal kink –9.5 0.65 1.0 1.056/1.749 0.022/0.063/0.108 0.23
intkink Internal kink –17.0 0.48 0.9 1.160/1.567 0.013/0.109/0.045 0.15

mixa Mixed kink –20.4 0.32 0.8 1.770/2.449 0.011/0.184/0.035 0.13
mixb Mixed kink –9.5 0.48 0.9 1.531/2.798 0.023/0.146/0.113 0.24

Notes.

(a)

is the averaged turns over the MFR, calculated by ; Φc(a) gives the turns on the surface. Here, Φc(ra) is based on Eq. (20). The values in this column serve as reference values only because these values are based on formulae for straight MFRs. More reliable twist profiles are discussed in the text and shown in Figs. 2, 8, and 13.

(b)

Minimum value of β in the whole simulation box; values of β at points (0,0,Rd) and (0,0,Rd−1.1a), which represent the internal and external environment of MFRs.

(c)

τa gives a typical timescale for the Alfvén wave to cross a distance d, i.e., it equals d/vA, in which the Alfvén speed vA is evaluated at (0,0,Rd−1.4a), just underneath the MFR.

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