I know the fact, that a husband and wife are told to distance themselves while a women is on menstruation, but what and how can a man satisfy his sexual desires?
I have come to a point where I cannot focus. I live near arctic circle and it is Ramadan and I can hardly get to have a private time. So now it has come to a situation, where I cannot focus on myself.
What ways or method Islam has allowed to get over a situation like this besides wait?
Now that you cleared your question, as menopause isn't a reason to stop having intercourse. While menstruation indeed is a reason, as stated in the comment of brother Zia, but that doesn't mean that you must avoid having any sexual pleasure or tension.
In the following I'm assuming that you are not considering a second (etc.) marriage and just look for legal pleasure during the menses of your lonely wife!
In fact you may have pleasure without penetration as we are taught by ahadith like:
In Sunan abi Dawod:
...What is above the waist-wrapper is lawful for you.
In al-Muwatta':
... "Let her wrap her waist-wrapper around her lower part and then he may fondle her if he wishes." ... (See also)
In sunan an-Nasa-i:
"The Messenger of Allah (ﷺ) would fondle one of his wives while she was menstruating, if she wore an Izar (waist wrap) that reached halfway down to the middle of her thighs or to her knees." In the narration of Al-Laith: "Being covered with it." (See also in sunan abi Dawod)
And read this clear hadith from sunan ibn Majah which gives an explanation on the verse about menstruation:
"They ask you concerning menstruation. Say: that is a harmful thing, therefore keep away from women during menses.(2:222)" The Messenger of Allah said: "Do everything except sexual intercourse."
An other hadith from sunan abi Dawod:
...What is above the waist-wrapper, but it is better to abstain from it, too ... (note this hadith is qualified as da'if)
See also this hadith in sahih al-Bukahri and Muslim.
Note that on the other hand there are many hadith which qualify intercourse with a woman in her menses as haram or kufr. But in case one committed this sin there's still a kafara for this.
So from what i quoted one is allowed to have sexual pleasure and be intimate with his wife, but he should avoid having intercourse, in the ahadith our Messenger (peace be upon him) insisted on the fact that his wives or women in general hide their private parts with a cover or covered them. So touching the wife on a tissue or on cloths is allowed even on the private parts (at least some scholars allow this according this Arabic fatwa based on the agreed hadith from both sahihs). While it is clearly allowed to touch and fondle what is above the naval and under the knees.
Also read this fatwa on the limits of intimacy.
And Allah knows best.
i think probably it is ok to make several days of additional fasting. there is hadith about fasting for unmarried young people.
you can see hadithes at https://sunnah.com/search/?q=marry+fast .
for example one of the hadithes:
Sahih al-Bukhari 5066: Narrated `Abdullah: We were with the Prophet (ﷺ) while we were young and had no wealth whatever. So Allah's Messenger (ﷺ) said, "O young people! Whoever among you can marry, should marry, because it helps him lower his gaze and guard his modesty (i.e. his private parts from committing illegal sexual intercourse etc.), and whoever is not able to marry, should fast, as fasting diminishes his sexual power."
You can marry another 2 or 3 women if you can keep balance among them, this is the ultimate solution for you.
