appending array to FormData and send via AJAX

You have several options:

Convert it to a JSON string, then parse it in PHP (recommended)

JS

var json_arr = JSON.stringify(arr);

PHP

$arr = json_decode($_POST['arr']);

Or use @Curios's method

Sending an array via FormData.

Not recommended: Serialize the data with, then deserialize in PHP

JS

// Use <#> or any other delimiter you want
var serial_arr = arr.join("<#>"); 

PHP

$arr = explode("<#>", $_POST['arr']);

You can also send an array via FormData this way:

var formData = new FormData;
var arr = ['this', 'is', 'an', 'array'];

for (var i = 0; i < arr.length; i++) {
  formData.append('arr[]', arr[i]);
}

console.log(...formData);

So you can write arr[] the same way as you do it with a simple HTML form. In case of PHP it should work.

You may find this article useful: How to pass an array within a query string?