The Satan and his limitations on Yom Kippur?

Question

The Gemara in Nedarim 32b famously writes:

״הַשָּׂטָן״ בְּחוּשְׁבָּנֵיהּ תְּלָת מְאָה וְשִׁיתִּין וְאַרְבְּעָה

The letters of the term "HaSatan" ("The Satan") is 364 in numerical value, [which equals the number of days of the year, except for Yom Kippur, during which he has no power].

And yet in the emotionally charged tefilla before Mussaf, Hineni, the shaliach tzibbur says:

וְתִגְעַר בַּשָּׂטָן לְבַל יַשְׂטִינֵֽנִי

May you denounce the Satan that he not impede me. (Artscroll translation)

When I asked someone as to how we understand this point of the tefilla in light of the gemara above, he answered that the chazal does not mean that the Satan is not there, but rather he is not שולט, i.e. has no dominion over us.

With this in mind, do any sources point to the status of the Satan on this day? What are his limitations so to speak? And if he is there, to what extent does he exist/do his "job"?

Answer 1

It says in Pirkei deRabbi Eliezer 46:

"Sammael said before the Holy One, blessed be He: Sovereign of all the universe ! Thou hast given me power over all the nations of the world, but over Israel Thou hast not given me power. He answered him, saying: Behold, thou hast power over them on the Day of Atonement if they have any sin, but if not, thou hast no power over them.Therefore they gave him a present on the Day of Atonement, in order that they should not bring their offering, as it is said, "One lot for the Lord, and the other lot for Azazel" (Lev. 16:8)"

From this Midrash it seems that Yom Kippur is both, the day in which the Satan has no power and the day in which he has davka the power over Israel. It is connented to the Sins of Israel and the "present" for Azazel is Hashems mercy for us,because the Satan is forced to accept this bribe and to be "busy" with the seir leAzazel instead of Am Israel on the very day that he has the power.