The Phrygian Dominant scale is the 5th mode of the Harmonic Minor scale. So if we’re talking about the second mode of the Phrygian Dominant scale, we're essentially looking at:
🔹 What is the "Second Mode" of Phrygian Dominant?

To find it, we take the Phrygian Dominant scale and build a mode starting from its second degree.

Let’s walk through it step-by-step:
Step 1: Define the Phrygian Dominant Scale

Phrygian Dominant = 5th mode of Harmonic Minor.

Example: E Phrygian Dominant is the 5th mode of A Harmonic Minor.

E Phrygian Dominant:
E - F - G♯ - A - B - C - D - E
Step 2: Build the Second Mode (starting from F)

Start from the second note (F) of that scale:

F - G♯ - A - B - C - D - E

Let’s analyze the intervals:

    F → G♯ = major 2nd (♯2)

    G♯ → A = minor 2nd (♭3)

    A → B = major 2nd (4)

    B → C = minor 2nd (♭5)

    C → D = major 2nd (♭6)

    D → E = major 2nd (♭7)

    E → F = minor 2nd (1)

So the scale formula from F becomes:

1 - ♯2 - ♭3 - ♮4 - ♭5 - ♭6 - ♭7
🔹 Name of this Mode

This mode doesn't have a widely used traditional name (like Dorian, Mixolydian, etc.), but it's sometimes referred to in jazz/metal/fusion contexts as:

    Ultralocrian ♯2

    Or Superlocrian ♯2

    Or simply Mode 6 of Harmonic Minor (because it matches the 6th mode of Harmonic Minor)

It’s a highly dissonant, exotic-sounding scale, sometimes used over altered dominant chords or diminished contexts.
Summary:

    The second mode of Phrygian Dominant is:

        1 - ♯2 - ♭3 - ♮4 - ♭5 - ♭6 - ♭7

    It corresponds to the 6th mode of the Harmonic Minor scale

    It’s sometimes called Ultralocrian ♯2 or Superlocrian ♯2

Let me know if you want fingerings, applications, or examples!